I guess I understand your POV, in which the music is not separable from the game as a whole. To me they are separable.
Most computer games can be played by a deaf person without any workaround, but few games could be easily played by a blind person (without some intense hack).
You can play it, but sometimes the music is a part of the mechanics (for example, in many of Frictional Games' survival horror games, the music changes whenever an enemy is not present/mindlessly wandering/searching for you/chasing you, and that information is useful quite often when you're dealing with an actual enemy and sometimes it's used to trick you even when there isn't an actual enemy), and sometimes it has subtle meanings (can't think of an example from any specific game right now, but at least in theory it would be possible to use a theme associated with a character's death when another character finds out about a board game called Dominion to imply that his previous life has come to an end or something, and a lot of games use music that's inspired by other music to create connections, for example Jade Empire uses music that's clearly influenced by Far Eastern music).
Plus, there are games in which music is actually the primary thing (like music videos, but with games instead of videos).