Game Center service is alive and well in the latest iOS beta, 4.1 beta 3, and as those beta releases get more frequent, we get closer to the release of this "social gaming network" for iPhones and iPod Touches.
Unfortunately, with beta 3, we now have to further specify precisely which iPhones and iPod Touches will be supported by Game Center. Originally, Game Center was expected to run on the same iPhone / iPod Touch hardware that iOS 4 would run on, which only excluded the original iPhone and original iPod Touch. Now, perhaps in response to user complaints about the how poorly the iPhone 3G and 2nd-gen iPod Touch run on the new OS, those two (far more popular!) devices have also been stripped of Game Center compatibility in the latest beta.
Since this is getting confusing, we'll recap. You can use Game Center when it launches later this year only on one of these products: iPhone 3Gs, iPhone 4, 3rd-gen iPod Touch ... and that's it.