I started to write one answer, and when I went to think of the actual specifics came up with a realization that my answer was wrong because of the nitty gritty of specifics of your example. So I'm going to give two answers, one answering what I think you intended to ask, and one answering what you actually asked; just to cover all my basis.
Can Aliens interpret visual stimulus without eyes
Say the aliens have a tv in front of them playing a tvshow, will they know that it is something more then a box?
The answer to this is yes, almost certainly, because they already are doing it. When you get down to it there really are only about two ways of interpreting information. Physical contact and electromagnetic. Sound is just interpreting vibrations within the thing that is physically connected to. Smell and taste is just thoroughly analyzing specifics of the object (in the case of smell very very tiny objects that drift through the air).
The point being that, whatever their normal senses are, they likely are aware of the other options available. In particular since the 'physical contact' option does not work in a void like outer space they must use electromagnetic radiation if they want to broadcast data across space. Any space fairing civilization must therefore regularly use electromagnetic radiation, and surely even non space fairing will for the same reason we used radio waves and the like, it's a much faster means of transmitting data.
Sure they may tend to use lower frequency waves, like radio waves, predominately, but they will surely have an understanding of the full spectrum. It's just a matter of realizing they should look at the part of the spectrum that is visible light to us to understand what we are seeing.
After that it make take some work to figure out how much nuance we put into color, but that's not really an inability to detect or understand light, but an interpreting the human psyche and how much importance it puts on that variance of light. It could take some time to derive how humans interpret the wavelengths to better understand the meaning we are getting out of it, and what meaning we don't get, but they should be able to do that if they watch enough of our 'tv' just by seeing what we bother to recreate and what we don't.
Now this is a technical understanding. They may not fully 'understand' what we are seeing intuitively. For instance we know dolphins and bats use sonar, we can discuss how it works and we can even create and use our own sonar sensors, but we as humans may not fully grasp what a bat is 'seeing' with their sonar. We know most of it, but there will be some nuance lost, and the knowledge will be less direct. They will likely 'watch' our videos by translating them to their senses and will likely lose a little of the nuance in that translation, but their get enough of it.
Now...as to the actual answer...
Can Aliens understand our video transmissions
Edit: I have messed with the below quite a bit. I mostly moved my paragraphs around to try to go with a more logical progression along the 'network stack' from low level to high; rather then the random flow-of-thought approach of listing whichever hurdle I thought of next I had before. I've also expanded a bit, added another point or two and tried to better stress the biggest problems. I also asked a question here that is relevant: https://reverseengineering.stackexchange.com/questions/11417/how-hard-is-it-to-interpret-binary-data-of-a-new-and-unknown-format-if-its-unk/11423#11423
The answer to this is probably not, and if they can they are massively beyond us in their computer technology and techniques.
One thing to keep in mind is that we don't broadcast 'video data', we broadcast binary data. A bunch of 1 and 0, nothing more. We later combine that binary data into visual data using an algorithm which the receivers know, but the alien wouldn't. Thus what he is looking at is some 1 and 0 and it's up to him to understand what that means. Those 1 and 0 could be video, audio, pictures, text, instructions for a program, or just gibberish; to name just a few things that the 1 and 0 could become.
To give you an idea of what I'm talking about sometime take a video file on your computer and open it up in a text editor like word or notepad++. It will look like gibberish, that's what happens when you take the 1 and 0 and use the wrong approach to decompiling them. The data only has meaning if you know ahead of time what data it is, and how to interpret that data.
This is the really hard part, which I struggle to express the difficulty of. You can do little but guess on how to interpret these bytes and see if the result looks right. If you decided we are broadcasting sound you could likely translate the video as sound to get something that sounds like a consistant sound wave. Since you don't know what our voices sound like you may think we have complex modulations of voice and spend hours upon hours trying to infere our language and syntax; all because you guessed wrong what those 1 and 0 were. You might instead decide that those 1 and 0 are some mathmatical code being sent to you and try to decrypt the seemingly random math, and since there are some consistency in video there likely are complex mathmatical algorithms you can perform on video to get nice clean numbers...which are wrong. Maybe you decide those 1 and 0 are sonar data, because you 'see' by sonar and that's an obvious way of seeing data. You may decide our color encoding is actually an encoding of how far away something is and how 'rough' or 'smooth' it is. You could get a valid sonar picture this way, but it probably isn't the picture were sending. Trying to guess what to even interpret the data as is nearly impossible, before you get to the fact that we have complex ways of encoding that encrypted data.
And now his lack of eyes comes back to haunt him, because he doesn't know what video looks like. Even if he somehow stumbles upon a correct way of reading our data he may not immediately recognize it as logical and toss it out to try a different interpretation; because he has so many to try and no way of being certain that one was right. Basically he expects to see us encoding data that fit his senses. When he has to guess how to translate our data his guessing the data encodes for a sense he doesn't possess seems unlikely. He will keep trying to tweak our video data to make sense as sonar because it looks like it could encode sonar (I believe that since video data is just reflected light and sonar is reflected sound their have similar levels of entropy and mathematically look quite 'similar', and this is likely true for many other potential senses your alien may use) and he understands sonar and it seems more likely he just hasn't cracked how were translating to sonar then that were using something truly foreign that he has a harder time of conceptualizing...
And if that wasn't already heard enough (and trust me, this is by far the hardest part) this is only after you have done a dozen other decrypting steps; because there are a dozen abstractions that you have to interpret first. Each one is a challenge, and each one adds more uncertainty that he is looking at the right data to begin with, and more possible interpretations of the data he would have to mess with, even more chances of 'false positives' where he comes up with some way of messing with the data to make something that 'looks logical' but is still completely wrong.
For starters, presumably our video data has some level of compression in it (yes I know UDP video on the internet doesn't, but I think most over-the-air video does for bandwidth reasons?). this adds another layer of logic. First you have to properly figure out our compression logic before you can start on understanding out actual encryption...though I would need to know what format the video is in to know rather it has any compression...
Which brings up another issue, how does he know which signals to look at? Were broadcasting multiple different types of video, as well as audio, pictures, and plenty of other signals. How does he know that all these broadcasts are using one encoding and all those are using another? what if he decides two different encoding are the same type and tries to come up with a viable method of decoding both? The most obvious example of what I mean is actually our TV. When we broadcast TV we are actually sending two types of encoding, audio and video, which are all in the same binary packets. It will take some work to figure out that all this data, sent at the same time, is actual representing two very different things. it seems more likely he will try to interpret the audio and data as a single 'feed' at first.
Going up one level of the network stack, imagine the alien is expecting trinary data he could get a very different interpretation of the data (though admittedly, presuming binary would make a decent amount of sense). If he misjudges the size of our bytes (think the minimum size of data we usually use) he will get very wrong numbers and projections. If he confuses big and small endian (basically, which side of the 'byte' represents big number changes and which represents small, or even more simplified should he read left from right or right from left) he will get all our numbers wrong by seeing small numbers as big and vice versa. If he gets his endian nature wrong then even if he translates our videos He could get bizarre video where all light objects are black, all black is white. All greens are purple and all blues are yellow etc. (okay, this is presuming a really simple version of video encoding, I'm sure were using a more complex one for broadcasting, but you get the idea...).
The point is there are lots of small things we take for granted when reading binary data because humans have standard conventions that we have agreed on, but the aliens aren't aware of them. Every one of these conventions is, by itself, not that hard to figure out with some static analysis, but having to figure out all of them, and not having a way to confirm your guesses are right until you have done all the other steps to decode the data, just makes things harder. It's an added layer of abstraction, and more importantly another layer of "hmm, I wonder if I got that right?" which could cause them to be less confident in everything else, and perhaps give up and try a different byte size or endian when they aren't getting data that makes sense to them.
If I go up further along the network stack there is the question of packets and where we divide them, as well as issues such as headers on packets etc. I won't go into this because I'm not as familiar with how broadcast binary does things, as opposed to how it's down on the internet, however, there is some level of abstraction here. Considering what I know about wifi I'm pretty sure that packets and headers will exist and need stripped off to get to the data, it's just a matter of what format the packets take.
To make things worse this assumes computer are infallible, and they are far from that. You don't realize it, but those 1 and 0 we beam to you are wrong. We send out a 1 when it should be a 0 here and there. Some random electro magnetic interference happens to collide with the wave were sending out and makes a 0 look like a 1 etc, the point is that our 1 and 0 can get swapped, and do. You don't notice that because we have fancy systems to correct for bad 1 or 0 by looking at the 1 and 0 around them usually. In the case of broadcast video data most of those auto-correct tools aren't there, instead we simply let some of the 1 and 0 be wrong because the human brain will figure out the picture even if one pixel in the corner of the screen is a shade too green for a split millisecond. However, these errors would make it hard for someone who doesn't know what he is expecting to understand the picture, because every time he thinks he knows how to read those 1 and 0 he will run into a bad bit and will think his theory on how to read it is wrong, rather then that the bit is just bad.
And of course this assumes he has the 1 and 0. Our binary data has to be broadcast as analog. He has to figure out how to translate analog to binary. This is complicated because our analog signals have their own error correcting logic in them, so he will have to figure out how to interpret that error correcting logic and filter it out before he is looking at the real analog signal which he needs to translate to binary....
And if that isn't bad enough by the time he gets it presumably the messages have been broadcasting for awhile, which means that the signal is quite week (the signal strength degrades exponentially with distance), They are going to need a Very Large Array, of an extra special value of 'large' to hope to get anything recognizable as something other then noise from any real distance, but even then the noise to signal ratio will be huge; and thus figuring what is our actual signal and what is background noise is going to be nearly impossible. Correcting for background noise is why we add in all those error correcting tricks he doesn't know how to utilize; but even if he knows how to use them as the signal gets weaker corrupted data because increasingly common because all our fixes are not foolproof.
Frankly the exponential decay of signal strength alone pretty much makes this question impossible, if they are far enough away that we haven't detected their mother ship in the sky odds are our signals are so degraded that a people with our level of technology isn't going to be able to correct for the noise...I think; I admit this isn't my area of expertise but knowing the degree of 'decay' expected for 'local' signals, and the exponential rate that power levels drop, I think it's reasonable to say it doesn't take much distance to degrade regular signals to a worthless strength. Random guess, no one further then the moon is likely to get much out of our signals?
The point of this being, our theoretical alien scientist has a much harder problem then interpreting video from a TV, he has to figure out protocol on top of protocol on top of protocol which we use to give meaning to our messages. Without having the dozen+ layers of understanding his figuring out how to get video out of our broadcast signals is nearly impossible. We can't do it, or anywhere close. I once worked on a project designed to help translate electromagnetic signals received if we didn't know the original protocol being used. Even knowing all our standard protocols just figuring which protocol we were dealing with was a massive challenge, and ultimately came down to "it looks most like protocol X, so lets try using X and see if that works". If he doesn't know that protocol X, Y and Z exist then he can't try one and see if it exists. He has to try every possible way of interpreting 1 and 0 (and I can't being to express how exponentially huge that number of interpretations is) until he gets one that looks 'right'. This was only solving one of those half a dozen+ layers of abstraction the alien would have to solve. And keep in mind after all of those layers of abstraction he still has the original, difficult, problem of trying to guess what our original signal was encoding to begin to guess what the decoding should look at; you know, the real challenge.
All along this path there is a very real chance of false positives, coming up with a wrong interpretation of data that looks reasonable enough that they think it's right. The permutations of possible interpretations are so huge that the chance of one of them being 'good enough' is high; particularly if the aliens expect us to have degraded signals and can write off a certain percent of bits that don't make sense off as 'corrupted data'.
The aliens would have to have truly impressive computers of the likes I can't begin to imagine to be able to come up with anything useful out of our captured signals. Computers to try all the many permutations of possible views, and computers able to analyze which permutations look 'plausible'; because no human, or set of humans, can reliable try all of the possibilities when there are just sooooo many possibilities.
I can say by the time the aliens have the sort of ability to figure out anything from our broadcasts they likely have a smart AI intelligent enough to figure out what all those light waves mean, in fact it would have to have already done that to know it had the right interpretation. If they somehow decode the signal then yes they will know how to interpret it; but I'm quite skeptical they will decode it.