How to find more Game Center games on Mountain Lion?
If you open the Game Center app, at the bottom of the Games tab there is a "Find Game Center Games" button:



Which goes to this page which has a list of Game Center games (there are currently only 8).

Also, some apps on the App Store will mention in their description that they have Game Center support. And you can see some games are featured with text saying they've been updated to support Game Center: