Hello richbrowngravy,
Welcome to Apple Support Communities. We understand that You're having issues removing your Game Center account from your Mac, and we'd be happy to help.
So we're on the same page, can you tell us what is the exact steps you followed to disable your Game Center account?
Please go to: Apple > System Preferences > Internet Accounts. Select "Game Center" then press "-" at bottom, and click "OK" when you get a pop up asking if you would like to delete your Game Center account.
for more information about Game Center, please check this out:
Play games on your Mac
We hope this information is useful. Kind regards.