To get an MPEG-2 480p movie down to 8KB, you would need something so sophisticated, it would be able to reproduce shapes and colours from a small data structure of some type.
There's a theoretical maximum for compressibility of data, though. And even with lossy compression, there's a level at which you entirely lose the signal. It would be fairly easy to compress something like, say, 10 hours of a black screen, because there is little information in there, but once there's any actual information (like video), it is simply impossible to compress that, lossy or otherwise, without destroying the signal. Video can usually be compressed to some degree, because information repeats and is shared between frames during motion, but there's a limit to that.
Now, there are ways of referring to data that are much smaller than the data itself. For instance, something much smaller than 1k can reliably refer to any movie I have on my hard drive already, and it's called a filename, but obviously, it isn't the actual data, just a pointer to it.
Claims like this remind me of the Borges story
The Library of Babel, in which the universe is an infinite library containing every possible text. However, the vast majority of them are, as a result, entirely incomprehensible bunches of random letters, with only the rarest of books containing anything recognizable at all, with it strongly implied that even those are basically just random noise.
One book, which my father once saw in a hexagon in circuit 15-94, consisted of the letters M C V perversely repeated from the first line to the last. Another (much consulted in this zone) is a mere labyrinth of letters whose original manuscript has neither numbers nor capital letters; punctuation is limited to the comma and the period. Those two marks, the space, and the twenty-two letters of the alphabet are the twenty-five sufficient symbols that our unknown author is referring to. The penultimate page contains the phrase O Tine thy pyramids. This much is known: For every rational line or forthright statement there are leagues of senseless cacophony, verbal nonsense, and incoherency.
My comparison to compression is this. Suppose you did have such a Library. You could "compress" any data by simply referring to it by something like a filename, referring to one of the books in the library that matched the location of the book you wanted, since every possible book would exist in it.
A mathematical proof is beyond me, but it seems intuitive that because of the vast number of such books, the process of actually referring to the specific book in the Library would require
as much information as the book itself contained.
There isn't a shortcut around this.
Similarly, "guaranteed" compression schemes are bogus. One class of data simply can't be compressed, and that is well encrypted data, which for one thing, has a flat histogram, i.e. is indistinguishable from random noise. Compression, by its nature, seizes on things like repetitions and similarities to be able to use short-cuts to refer to the data, and encrypted data (or noise) has nothing like that to shorten.
Video does have patterns and recognizable repetitions like this that can be used to shorten the data representing it, but eventually you get down to what makes that particular video unique, and beyond that, you can't compress it any further.
So compressing a whole movie down to something like 8K just doesn't work.
As you point out:
it would just have a single-byte command saying "draw circle".
Except really, when you're getting down that small, I think you'd basically be requiring the algorithm to be able to fit commands like that into a single bit. So in other words, "draw a red circle 5 pixels in diameter," "draw a purple dodecahedron 9 pixels on a side," and thousands of other possible codes. But you have to fit all of these into 0 or 1. Not a string of 0s or 1s, but one single solitary bit.
It's basically a perpetual motion machine for compression. It can't possibly work and nobody who actually invented such a thing, even if they just keeled over dead, would have failed to leave something behind that would give some indication how it could work.
I've probably given this too much thought for it being absolutely transparent bullshit.
