iOS 9 beta caused some game center issue, where game center doesn't login properly and the settings for game center won't load ... not sure why, any idea ?
I noticed only devices which were update to iOS 9 beta then to official iOS 9 had that issue, I updated other iPads and iPhones to iOS 9 today, Game Center works just fine on them!
If you are having similar issue, please join the thread ( https://discussions.apple.com/thread/... )