Apple has removed Game Center functionality on ALL versions of OSX so C&C: Generals Deluxe on the MAS is a single player ONLY experience.
Apple has removed Game Center with OSX 10.12 (and iOS 10) so we recommend stocking up on adding friends BEFORE updating.
Our apologies for any inconvenience this may be causing. We've logged this issue with Apple and are awaiting an update from them to fully resolve it.
In the meantime, please log out of your Game Center app account and disconnect your internet connection.
Relaunch the game and it should then load properly.
Please "follow" this article for updates as they are available.