If it were about doing something fundamentally new (or something that hasn't been explored much), then i'd probably go for something that isn't really a "game" as we currently understand it.
For example, after playing the interactive fiction "galatea", i thought that while it was awesome, it just scratched the surface of something really new: In usual games, the players (not his characters) personality and psyche is taboo. Also, there typically is a strong distinction between the players char, and the other characters (a "me/you"-distinction). Galatea began to blurr those barriers, and i found that really fascinating.... suddenly, the players own worldview and psyche was no longer offlimits... galatea began to question the player based on what he did. Made the player introspect and think about his life and consciousness. It was less a "game" but more a dialogue between the player and an AI.
I began making detailed drafts about how one could go further into this direction, by allowing even deeper questions at the player, implementing a behaviouristic "emotional" model for the AI, spicing up the imagination with scene-images that would not be there to show stuff, but to imply an atmosphere.
I also wanted to allow even more intense actions by the player (including equally intense consequences - my idea was to let the player do what he wants to do - no matter how dumb or morally questionable it may be - and them leave him to the consequences - which in some cases would be nightmarish and in other cases more than wonderful). I also had an idea how to blurr the line between "me" (player) and "he/she" (AI) to the point where there almost is no difference anymore.
In the end, i decided that existing programming languages would not let me implement something like this optimally - and thus prefered to put this "game"-idea on ice, until another project of me - a programming language - is in a usable state.
P.S.: Hmm, i guess with all those infobits, the overall message may have been lost a bit. What i was trying to say, is that one thing that i would be interested to explore more, is "games" that aren't about "winning", but about exploring oneself - basically tools and simulations to introspect and think about one's own life. Not in the sense of an author telling the player something, but instead just giving the "player" scenarios and questions, which the player can then explore himself.