So, I was looking at this: incredibox.com
If you don't have sound or Flash, it's essentially a short song with two dozen or so short tracks that loop infinitely. By adding tracks in, you create a song. You can even "play" the song by removing and adding tracks live, giving a sense of progression and thematic repeats and so on. "Shuffle" mode does it automatically, creating an endless song that, while it never really goes anywhere, is very listenable.
The visual is great, too, but let's talk just about the audio.
I was thinking about this. The reason it can happen is because we have very structured music. We can build tracks which get along with each other in great quantities: you can add eight or ten tracks to the mix and it still plays okay. The structure allows us to make sure every track gets along with every other track.
It's possible to do the same with a game, if the game is also structured so the play elements get along.
For example, let's imagine a shooter where you play with just your left hand - you steer the ship, it automatically fires. Waves of enemies and obstacles sleet down the screen.
On the right side of the screen are a number of "tracks". These are different progressions of enemies and weapons attached to your ship. So if you turn on this track (using your right hand/mouse), you get the sine-wave enemies. If you turn on that one, you get the big bombers that come to midway down the screen, shoot a halo of shots, and then retreat back up.
You can even make tracks modify other tracks. This track makes every third wave of enemies bright green and fire homing shots instead of normal shots.
The ones that give your ship weapons make the enemies drop weapon power-ups which work just like normal games, upgrading one weapon or switching to another weapon, granting shields, satellites, etc.
For added joy, also do music, as with the link above. Also possible: bosses. Also possible: sharing "compositions" with others.