I am trying to disable Game Center on El Capitan
To disable Game Center on Mac OS X:

Open Game Center. In the menu bar, select Account > Sign Out. If you don't want to sign out, you can instead click Account > Settings, then uncheck "Allow Invites", "Nearby Players", "Contacts", and "Facebook". After you've done one or both of these two things, go to System Preferences > Notifications > Game Center > Game Center alert style > None.