Relativistic Asteroids is just Asteroids -- but with (some) relativistic effects added -- specifically, length contraction and time dilation.
As your ship accelerates, the little triangle that represents it visibly shortens (length contraction), and if you rotate, contraction is retained in the direction of motion, but not the others.
Time dilation isn't particularly notable--except that your bullets travel a shorter distance (when fired in the direction of motion), presumably because, in their frame they "expire" more quickly relative to the reference frame.
Pressing "f" during play shifts from the reference frame to the ship's frame, meaning that the ship looks normal, but now the asteroids are foreshortened in your direction of motion. (That's why the asteroids appear flattened in the screenshot above.)
This is actually kind of cute, and an imaginative way to demonstrate some of the physical implications of Einsteinian mechanics (though not necessarily to provide any real insight into why things happen as they do near lightspeed).
Some relativistic effects are not simulated -- and a shame that they aren't because they'd be interesting. There's no red or blue shift; asteroids are all Asteroids green, whereas in real life, objects moving toward you at relativistic speed appear bluer than they would at (relative) rest, and objects moving away are red-shifted. Implementing that strikes me as not all that difficult, and visually interesting.
Also, it does appear that only the player's ship is foreshortened by its velocity; while the asteroids don't accelerate, of course, it does appear that their shape is not affected by their velocity.
Finally, the notion of the light cone is not represented; by default, "light speed" in the game is 6 cm/sec, and the screen is considerably wider than that. This means that, say, when we view the screen from the ship's frame, and an asteroid is 6 cm away, we should see it at the position it occupied one second ago, not its current position. From all evidence, asteroids are drawn at their "real" positions, regardless of light speed.
Fun game to play? No, not really; it's just Asteroids with some interesting physical effects that, to the degree they affect gameplay, simply make it a big more frustrating. But it's an interesting use of gaming ideas to get across physical ideas -- and its only real flaw is that it doesn't go far enough to represent the effects of relativity.