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Well it seems the app is gone as of iOS 10. Apple is now handling invites and challenges via iMessenger. Some of what was Game Center is still around in that it's still in settings and you can still change your Game Center ID, IF you manage multiple game accounts. (Clash of Clans people will understand, lol) But the icon and app are gone for good. I did a google search and found a bunch of articles about it...
https://www.google.com/webhp?source...1&espv=2&ie=UTF-8#safe=off&q=Game+Center+gone