If it lives under different conditions than we are used to, it could be a supercritical fluid. That is, a gas that's so dense that it would be the same as what we think of as liquid. It doesn't actually have to be supercritical in that the gas is as dense as the liquid of the same substance. It could be truely a gas phase, but as dense as what we think of as liquid, say, water. Look at the atmosphere of Venus for example.
A fluid’s density in a closed system is what allows it to carry other particles. Pumping is affected by the ability of the fluid to be compressed. You want a heart-like pump, not a propeller screw, right?
But making it a supercritical fluid would be really cool, and could use something like a phase change heat pump as a heart!
In general, gasses have a density of around 1, and liquids of around 1000. A supercritical fluid has a density of 100–1000, and a fraction of the viscosity of a liquid.
In addition, there is no surface tension in a supercritical fluid, as there is no liquid/gas phase boundary. By changing the pressure and temperature of the fluid, the properties can be "tuned" to be more liquid- or more gas-like. One of the most important properties is the solubility of material in the fluid.
This gives a rich source of ideas on how material transport can work: pressure differences can make material go into solution or drop out. The lower viscosity compared to liquid and lack of surface tension means it’s easy to move through fine channels. It can diffuse much better than liquid, so it sounds like a good idea for circulation for the same reasons it is used in industrial processes (not limited like the trachaea problem for gas!)
Of interest to you, see the section on planetary atmospheres. How about an ocean of supercritical water with ice on the bottom? Is that crazy enough?
So you want a high pressure, and a high enough temperature so it doesn't just become liquid. The actual values depend on the fluid, and as explained in the article, you can mix fluids to get the point just where you want it. So the body might use blood that's right near the tip of the liquid/gas phase line, so its heart can induce a phase change in one direction and avoid it in the other, or exploit sudden differences in viscosity, to acheive pumping action.
See also Close to Critical by Hal Clement. His planet had an atmosphere/ocean near the critical point of water, but I don’t think he explored how biological processes could exploit that.
Spilled Blood — a vignette
ⶼ hollered as much in surprise as in pain.
He was drawing his bow and concentrating on the prey that they had been tracking all morning, when out of nowhere a ↭ attacked him! The ↭ is like a fat rope half a span long with a biting mouth on each end and a fin along its length edged in razor wire. One mouth grappled for purchase, teeth chattering against the tough scales on his drawn-back arm. Meanwhile the unusually supple body wrapped around the arm and the razor fin slid along the scales until it found an edge to catch on, slid under the scale, and sliced the skin.
Blood spilled from the wound, in a short burst. The rivulet pulled itself together into small glistening globules, flung a span away from ⶼ and his attacker. The mess slowed after the initial impulse and hung in the air right in the middle of the path.
The other two members of the hunting party quickly grabbed the ↭ by its heads, carefully unwrapped it, and tied it in a game bag. The oldest and most experienced of the party, ⶾ, tended to his bleeding friend’s arm with a preparation to more quickly stop the bleeding followed by a bandage. That left the youngster, ⷆ, to deal with the spilled blood. He dabbed at the arm with swabs, wiping and tossing into a small bag (part of the medical kit they carried) before it could evaporate. Then he had to deal with the initial spill.
The blobs hanging over the pathway had already grown to three times the original size and turned to fuzzy ocre knots of air. To any carnivore or omnivore, blood usually smelled like food. But their own species’ blood smelled disgusting. So it wasn’t just concern over attracting preditors that motivated him, but instinct that spilled blood is bad to be around. Just the thought of passing it through his gills was nausiating. So ⷆ closed off two breathing intakes and breathed only at his back, and approached the rapidly evaporating spill with an empty game bag stretched between two arms.
He flapped the bag up-down;up-down, moved a bit to the side and repeated. Again, and then closer in with a very careful left-right. The disturbance in the air reached the blood and ⷆ could see little whorls grab the knots and draw them out into twisted loops, only futher evaporating the drops. But then the entire area of the spill rolled over, smearing the blood into yellow fog, but rolled up into itself and not spilling further. Easier now that he could see the movement of the air, ⷆ carefully fed the vortex and sent it gliding away, several spans off the path and down to the underbrush.
The wounded ⶼ was squatting low: his three leg tendrals were coiled into a tight triple helix with the three points brought together, forming a single point that touched the ground. The body poised low to the ground over the point. Likewise, his arm tendrals were folded neatly and close to the body. It was important to stop any bleeding before the high pressure caused too much blood loss, and this included shunting blood away from the extemedies. Shock, in other words. Knowing he was in good hands, ⶼ relaxed into a meditative state, to give the wound a moment to close and recover normal activity level quickly. The thick oil applied to the wound also aids quick recovery—by the time the cleanup was done and the medikit stowed, it was safe to move normally without fear of losing more blood.
They continued on, without the meal for the village they had almost bagged. The ↭ was a small consolation prize, that would be kept for ⶼ alone. His family would prepare the meat in the least unappitizing way they could; eating it made a point and was not waste. The real value was in the inetable parts: Unlike most animals which had scales and scoots and other hard plates, the sinuous ↭’s hide produced a small piece of leather. The mouth bones and teeth were not favored for weapons but had uses in making certain tools, and the razorfin could be preserved and used as a tool in itself.
The morning’s prey was long gone after the commotion, so the party started over, searching for tracks. The village still needed meat.