At this point, Gamecenter is there to show your friends what you did.
It's up to the game developers to enable people to play against each other. It's not really a function of Gamecenter as not every game is multi-player. For example, FlightControl is a single-player game. You just match your high score against others.
It's possible that the Gamecenter backend simply isn't sophisticated enough to enable head-to-head competition at this point. At some point it may. You will probably need to exhibit a bit of patience with Apple, plus provide feedback to their development staff about your interests.
Yeah right about being patience, I need to be. But apple takes things VERY slowly. i.e getting 4.1 out for the iPad till Nov. UGH!
I have two games that they say there GC ready, one is showing up and the other isn't guess I'll go see what the deal is with that.
How do I provide feedback to Apple?