Games are like songs. Songs may have good writing and story, but insofar as they do they''re nothing more than a support for the song. The music and singing is what makes the song, just as it is with design and games. To the degree that your game''s focus is on story and character over actual gameplay, you are not making a game. You are making something else.
I disagree with you here on two counts.
The lyrics can make a song to some people (like me), and herein lies the problem for making a artistically satisfying game. It''s like the french dude said, some people aren''t going to appreciate it, these people are known as "normal gamers", there are very few gamers out there that will be able to make it a viable product. (no where near enough to support the amount of time and money you might have to put into a game with such ambition as to make people question and think).
A computer game can still be a computer game even if the focus is shifted from entertainment to artistry. Music is still music even if instead of creating a "popular" song you just create nice atmosphere or sound (ie comparing some dodgy band like Backstreet Boys to Vangelis). It''s just that the backstreet boys will suck to those people that like non-atmospheric music (and there are alot of them, that''s why we get more bands like those boy-bands than we get artists like Vangelis etc) and Backstreet Boys will suck to those who like decent older style artistic music.
It''s more a matter of audiences defining what is produced because the industry has become quite expensive and no one wants to take the time out of their life to really devote it to making a artistic computer game - and that''s what it takes to make art. Taking time out of life and really doing something that comes from within, it does not come from looking for a paycheque.