I hate genres in gaming. Anybody who has had a design class with me can tell you, there are few things I dislike more than genre. I have two major criticisms of the current genre system in games:
1) Design Ruts - As soon as a developer or a publisher says to themselves, "We are making an RTS" or "We are making an FPS", their heads are immediately filled with expectations for the genre. Specific little things that those games are "supposed" to have. I.E. resource management in a Real Time Strategy game.
2) Mechanical Classification - The system we currently has classifies games based on their mechanics, rather than their style or substance. As far as I can think of, we are the only medium that does this. Sure, maybe those more technically informed about films might refer to them based on the mechanics of the cinematography, but for the most part a film is referred to by its content. I.E. Drama, Comedy, Romance, etc.
I'm not going to blame the industry for this, or the game journalists, or anybody else associated with the medium. Traditionally, games have only been about the mechanics. Stories, characters, and context were so abstracted that they didn't really matter or could be summed up in a quick sentence. Truly, mechanics were the king.
Chess is about a war between two factions. Super Mario Bros. is a game about a plumber rescuing a princess and so on and so forth. It made little sense to categorize these things by their visual style or their thematic elements.
But now, we do have a lot of these things. Games have themes and visual styles, and I would call for a move away from the genres of yesterday. Naturally, that's an easy thing to say and much harder to do. I don't have a ready made list of categories to classify different strokes of games ; Ian Bogost at Gamasutra wrote this article about a style he would call "Proceduralism". I agree with many of the things he says, and disagree with some of them, but this kind of thinking will be an extremely useful tool for us designers as we go forth in an effort to make something new.