Sarah Perez, writing for TechCrunch:

With the introduction of iOS 10, Apple will finally allow users to delete the pre-installed apps – like Compass, Stocks, Tips, Maps, Watch, and more – from their smartphones and tablets. But there’s one app that you won’t need to remove: Game Center. Apple confirms that Game Center will continue as a service, but it will no longer be available as a standalone application on their devices.

From what I gather, Game Center leaderboards, friends, and challenges will still be available. But developers will have to build those views into their application rather than users having an all-encompassing app for those interactions.