Game Center login required to access multiplayer?

I just recently got Borderlands 2, not from the Mac App Store, but from a friend who bought in on the mac app store and gave it to me. It starts up fine on my computer, however, whenever I click, "Launch Game" I get a message saying,

Game Center login required to access multiplayer

The requested operation could not be completed because local player has not been authenticated.

Then it gives me two options. To play Single Player, which leads me into the single player game, or Sign in with Game Center, which takes me to the Game Center app, and just stays there. No login or anything. The message in the game disappears but if I click "Launch Game" it gives me the same menu. I want to play multiplayer with my friends. So, what does this mean, and how do I get past it?