Its only going to work with games that are on the Mac - integration with iOS is only going to occur with mutiplatform titles that the developer specifies as compatible. Think of a game like Angry Birds - their are distinct iOS versions for the iPad, iPhone, and the Mac.
You are not going to be running the iOS version on the Mac - Craig made it clear with the demo that the developer made a Mac version simultaneously with the iOS version. They will be dedicated apps.
We wont know any of that until ML is formally released and developers actually take advantage of game center to know exactly how we will know. We only saw one title - presumably of an unreleased game that has the same name across all platforms.