I decided this was a challenge to have fun with, so fun I had.
Tl/Dr: Okay, maybe too much fun. As Michael Kjörling pointed out, it could use a summary. The basic idea was that everything we tend to be comfortable with calling life needs a distinct outer edge, a membrane. You can pull this off with densities (like a creeping fog, or a temperature inversion layer), but it's really hard to get lifelike behaviors out of those within a 6x6x6 cube. The solution was to rely on the vortices of turbulent flow to form these membranes. As an added bonus, these vortices also provide an easy way to do molecular chemistry essential to using organic life. Add to that a set of enzymes (which may not be all gas, but make the creature a lot more plausible), and you've got something that might work after all.
There were two big limitations to the feasibility of this. The first is that vortices are inefficient. While a smoke ring may carry for dozens of feet before dispersing, the smaller vortices are always turning lots of energy into waste heat. This might be solvable by using the transition region between laminar and turbulent flow, but that's a really difficult to model region so I elected not to pretend I knew enough to make it happen.
The second limitation was that its hard to make life from nothing. Science doesn't know many ways to re-create life, it just has well documented ways that life maintains itself. Thus, every lifeform we see is part of an ecosystem that keeps it alive. No human would survive without it!
So, for the rest of this answer, I decided to try to craft such an ecosystem, designed to try to create just a glimmer of hope that such a creature could arise. I admit, I hammed it up a bit for literary effect, but I hope that it leads to the question, "might it be possible?" If so, I've done the best I can for something which has not yet been observed via scientific methods. If your instinct to disbelieve in such ghosts is the same level of disbelief one might associate with the Krebs cycle or T-helper cells if they hadn't been printed in a textbook, I've succeeded. The question will be enough to keep it alive. Enjoy.
I avert my eyes as I walked hurriedly past the old withered tree on top of Sorrow Hill. The village elders always said, "Cover your eyes on Sorrow hill," with such sincerity that nobody ever bothered to question them. The ground is littered with gopher holes; covering your eyes would simply be a one way trip to Doctor Mink for a sprain or worse. So I compromise, averting my eyes as I went on my way. It wasn't so spooky of a tree anyways, with the wind down and all. When the wind picks up, the wind howls through its branches and hollow trunk with a ferocity that makes it feel like its moans and cries try to pound their way into your soul, but with a light wind like this, it sounds like little more than wind dancing through the branches, though perhaps with a slight sinister hue.
Before we get to air-beasts that consume organic compounds, I wanted to start with a much different ghost. So the real challenge with a gaseous living being is that its really hard to gather what is known as negentropy, or the strange ability for a living creature to avoid falling victim to thermodynamics by consuming objects with low entropy and emitting waste that has high entropy. Life usually does this with a boundary, but gases can't do that well. Without a liquid or solid to form a boundary, gases tend to simply diffuse. Even if the gasses are different densities, so one floats on the other, they don't mix enough to do work.
Those generalizations don't quite apply when turbulence is involved. We've all seen pictures of extraordinary vortices, like smoke rings. Turbulent flow allows for regions to be separated simply by the varying directions of movement, and the ability to create regions makes it much easier to start arguing that such a ghost could exist.
As an added bonus, turbulent flow is so hard to model that Computational Fluid Dynamics programs typically have to approach it statistically. This means I can get away with a great deal of hand waving. Its hard to argue that a vortex cannot contain the informational structures needed to do the behaviors I suggest this ghost does. Without a clear argument why it cannot happen, the existence of such a ghost is right in line with the curious fact that non-ghost life exists. If you're comfortable with the rest of life, this ghost isn't too much of a stretch.
One big advantage I see of attaching such a ghost to a tree is that I have something which can rekindle the ghost if the wind dies down. If the ghost can do anything to shape the tree (such as eroding it with sand), it can shape the tree to encourage a new ghost to leap forth when the wind rises again. This feedback loop suggests that maybe, just maybe, its possible for this ghost to develop.
This is probably the most questionable part of the system. Is the carefully shaped tree part of the ghost, or just a part of the scenery that the ghost is attached to? Those questions get harder if we start letting the ghost store more and more information on the tree trunk. In the end, I decided it fit well enough with where I wanted to go with the answer, so I kept it. It also has a nice benefit of helping let the ghost be more sentient. One measure of sentience is the Sentience Quotient (SQ) which is a ratio of processing power to brain mass. A humans SQ is estimated at +13, and most neuron based brains are clustered around there. Plants weigh in at -2, except carnivorous plants which hover around +1. Given that this is a mass based measurement, gaseous brains are going to be challenging. Air is roughly 1/1000th the density of a brain, so its going to be hard to compete. It might drive the ghost down to a +10 (which interestingly enough, is really close to the SQ of IBM's Watson!)
The old man told a good tale of the air that is alive, ghosts of the most believable portion. He had us all laughing at ourselves, certainly every last one of us was thinking of the old withered tree on Sorrow Hill as he described them clinging to old trees as a bat clings to the roof of a cave. Such a story was good enough for a meal (even if one steadfastly dodged giving a name), but when he offered to get rid of our ghosts for a fee, he was going to have to do better than that. We were about to excuse him from our table when he tried to convince us anew. He declared one of these ghosts to be in the house right now! We responded skeptically. There was no wind in this how could there possibly be one of these sorrowful ghosts? He insisted there was another kind of ghost, a shambler, which fed on decaying and rotting corpses to subsist when the wind ceased to be. He demanded a live rabbit and he'd prove it! We didn't take him seriously until he plunked down a good fair trade in silver for one rabbit. Sarah went back to fetch him a nice sable while Father pocketed the silver.
Sarah came back, rabbit in hand. The old man took it in one hand, and with the other he reached for a crude syringe of liquid that he apparently kept handy for a parlor trick like this. He injected the liquid into a vein on the rabbit, whispering to it all the while. He explained that it was a bioluminescent material to expose the ghosts. He said it tasted bad to them, since it wouldn't turn into a gas, but it was hard to separate it from the blood, and if the ghost was hungry enough, he'd eat it anyway. He said a prayer, thanking the rabbit, and with a single fluid motion unleashed his knife from its sheath and sliced the rabbits neck wide open, letting the blood splatter out onto the floor.
Mother was furious. It would take her a lot of work to clean that blood out of the floorboards, and she prided herself on the house she kept. Father however, restrained her without a word, staring at the carcass of the dead rabbit. Already tendrils of bio-luminescence stretched upward as though in a vortex, but the vortex did not give the air of a natural occurrence nor a magic act. It arced over to the corner the old man had emphatically gesticulated towards earlier, and slowly took form. As the bio-luminescent material spread, a clear shape of a humanoid took form. Standing not ten feet away from us had been a ghost, the entire time, eager to feed on flesh.
The shamblers are more of the kind of ghost that you were looking for that feeds on organic matter. In this ghost mythos, they are a second phase of life for the ghosts, similar to how Jellyfish polyps become medusae. This form is not as concerned with longevity, because their "essence" is mostly contained in the parent wind ghost. Instead, it focuses on how it can get access to regions which are inaccessible to a wind ghost because there's not enough wind.
The shambler realizes there's a lot of power in organic compounds, and decaying flesh happens to emit a lot of them in already gasseous form. It would not be too far from possibility for them to carry along a small packet of enzymes to beak out exotic energy bearing compounds like sugars, and use them for fuel.
What are they fueling? Well, given that they are turbulent flow with vortices, we have something called vortex energy. Not to be confused with a metaphysical energy, vortex energy is simply energy that we know can be used by the vortex to do work (like sustaining itself), but otherwise acts just like thermal energy to be dissipated. If a shambler could minimize the dissipative losses from its chaotic flow, it could move forward like a smoke ring, and then use the organic compounds to generate energy to sustain itself.
I think this dissipation issue may be the major limit for this vortex based ghost fitting into the 6x6x6 volume. Small vortices always dissipate energy because the intermolecular interactions become non-trivial as the vortex gets small. As a solution, one might look into the transition region between laminar and turbulent. That's an eerie region where it seems anything is possible. I lack the physics degree needed to claim I understand this transition region, but it may admit enough feedback to support the ghost's "thinking" while being laminar enough to conserve energy.
A more realistic shambler would be less humanoid, and more like a whisp. Given just how essential keeping dissipation down is for such a shape, it'd certainly not be wasteful in forming a humanoid shape. However, for my story, I decided that the deep dark secret would be that a human actually taught the wind ghosts how to make shamblers, so they mimic the form he taught. The idea of eating organic matter seemed out of place, so explaining it as the misguided efforts of humans seemed simplest. Given more time, I expect these humanoid shamblers would eventually round themselves out to a more efficient shape, but it was fun to make them look scary.
Worth noting is that much of the need for intelligence in the wind ghost is the tremendous complexity of creating these shamblers to consume organic matter. If the question did not require organic matter, then you could get away with a wind ghost that is less capable at defending itself and instead relies more on replication from tree to tree, which is a lot easier than combat. (the OP did say I could relax the organic requirement, but I figured I'd make a stab at it, even at the cost of risking more "that could never happen" responses)
The village has a pulse of its own. Sometimes it doesn't seem to be fully rational. In less time than I ever thought possible, news had spread from a ghost in our house to a village wide call to destroy the ghost of Sorrow Hill once and for all (never mind that it was still a wives tale for most before tonight. Mobs never seem to follow rhyme nor reason). With torches and axes in hand, the men of the village marched forward on a withered old tree, with blood in their eyes. The wind whipped and howled around them, threatening to extinguish the torches, but they pressed on.
As we reached the bottom of the hill, the tune changed. It was a windy night, whipping up dirt and dead plant matter off the ground into our faces. Some were even forced to cover their eyes as they ascended towards the tree with murderous intent. They were the lucky ones. I watched from my position in the back of the mob, hatchet in hand like a good boy. From all around vortices began to touch the ground like small tornadoes. Where they landed, they picked up what looked like dust from afar. Whatever it was, it was clearly sharper than dust, for when the vortices flung them at the eyes of the men, their cries were sharper than expected. Like from a horror story, the vortices began drawing away blood and virtuous humor, leaving the eyes of the doomed like withered grapes in their eye sockets. The horror story was not over. Whatever it was that made those cursed tornados lift up arms against us began to change the mixture of bodily fluids, spinning it out, distilling it into its various components. After the most morbid lesson in chemistry a boy could ever have, some of the liquid lept forward at the second line, driven down their nostrils and into their lungs. That chemistry lesson left them wide eyed and stunned, coughing up blood and foam which was quickly whisked away for more.
A lot of families will never forget that night. Not ever.
What would a living creature be without the ability for combat, to protect itself. In this case, I draw attention to the fact that vorites are usable to separate compounds of different molecular weights. In fact, the same principle is used in centrifuges to enrich Uranium! Imagine the chemistry your body could do with a centrifuge at its disposal!
The sharp sticks and twigs are probably the nicest way to tell people to back off. Using their own body chemistry against them is just rude. I left a fair bit up to the imagination, but it seemed reasonable that a living being's defensive mechanism could involve conjuring up enough "blood magic" to make something like Mustard Gas, concocting it in whirling vortices rather than Erlenmeyer flasks.
"Four tons of silver!" Phil, our village leader, roared. "Four tons of silver for an exorcism? How would you even carry that if we gave it to you?" Our own foolish endevours had shaken the town, leaving Phil in the unfortunate position of having to act strong (an unfortunate consequence of an elected position). The old man calmly looked straight back at him, said "I have my ways," and went back to calmly not responding at all to Phil's bravado. I have no idea why, and maybe Phil can tell you more, but this shook Phil quite a bit, and he toned down. "This village doesn't even have four tons of silver, and Sorrow Hill certainly wouldn't be worth that price." The old man leaned forward. "Then perhaps a different offer: four ounces of gold, and I'll need a favor from you." Phil considered it: "what favor?" Cryptic as always, the old man simply said "You'll get to know when I need to claim it. That's how favors work."
The old man had demanded everyone stay inside while he worked, explaining that the ghost needed to not sense him coming if he was to succeed. Everyone dutifully went back to their houses, but I dug under the floorboards for just such an occasion. Slipping out without Mother even noticing I was gone, I followed the old man downwind -- far downwind. We must have gone a full mile before he finally turned toward the tree and began a slow walk towards the Hill. He was certainly in no rush to earn his four ounces of gold, but he walked with purpose. It seemed not a hair was out of place when he walked, everything advanced forward in one smooth movement. I made sure I stayed well behind, and just for fun, I tried my best to imitate his slow purposeful walk as I followed in his wake.
As he got to the Hill, his movement became more advanced. Where he once simply walked forward, he now fluidly danced this way and that, gesticulating with circular motions like a caterpillar reeling its cocoon. Always forward he advanced, never taking a step back. He continued this advance until he was within reach of the tree trunk. His hands flexed like cat's claws, then stretched outward like a bird's beak. Finally, with no pomp nor circumstance, he simply reached out and took hold of part of the trunk. The response was swift. Tornadoes of wind rolled forward, grabbing the sharp thorns and sticks from the ground and lining them up towards the old man, but he stood there quietly, unmoving. The vortices of dangerous sharp objects twisted this way and that, like arms trying to find a way to strike, but found none. Then, in a visible fit of rage, it struck out towards the old man. The old man simply fell out of the way, dodging them entirely, but in the process tore free the section of wood he was holding onto. The tornado arms reached forward, and then choked, like they were no longer part of something greater. Soon they could no longer hold onto the sharp matter in their grasp, which fell to the floor. In the end, nothing but the howl of the wind remained, and with a less sinister tone at that.
A wind ghost is going to need to be very aware, if it is to protect its precious eroded tree. This goes doubly so for an adversary approaching from downwind, where it will be harder for the ghost to send information back upwind to protect itself. In this case, the mysterious old man is simply walking in a way which doesn't disturb any of the eddies which make up the ghost, so the ghost literally can't see him. This is harder up close, where the eddies are closer together.
As a flair, I decided this old man was going to give the ghost a chance to mend its ways, and become "good." Instead of just breaking the tree right away, he gives it an opportunity to change instead. In the end, it strikes, and its own strike leads to the tree getting broken.
The village was more than content parting with the four ounces of gold as payment to be rid of all but the cursed memories of the ghost. Phil inquired as to the favor, but the old man waved it off. "Don't worry about the favor. It is taken care of." Phil looked confused, "But we haven't done anything yet!" The old man smiled, a true and genuine smile: "Some of the most powerful favors are those you aren't even aware you are doing." He stared straight through me, even though I had been half hiding behind Mother's skirt. He pocketed the gold, gave us a wave, and started down the road to the next town.
I still remember what I saw that day. I practice the gestures I saw the old man do as he approached the old withered tree. Sarah thinks it's silly, and Mother looks at me funny as my fingers contort this way or that, but I think it's worth it. Maybe some day, I'll be the one to ask a village for a favor. Maybe.
I think a lot of the feasibility of such a ghost depends on the environment. We already know that the Earth has given birth to some pretty bizarre things that we now call "nature." A slightly different environment might encourage different outcomes. Personally, I find it a little bizarre that we can define little things called memes which only exist because we have constructed a communication structure with which they can easily find a home and replicate. Compared to that, a mere ghost seems pretty tame.