The iOS 4.1 Game Center is now ported over to the iPhone 3G. Game Center is working  fine with iPhone 3G on iOS 4.1. Below is the video of the new iOS 4.1 Game Center running on iPhone 3G, alongside iPhone 4 and iPhone 3GS.

Check out the Game Center in action below.

 

However, the feature was added in iOS 4.1 but excluded from the iPhone 3G. There was no exact reason given, and it was simply assumed that it didn't run well on the device whereas the video shows it works perfectly fine on iPhone 3G.