Used to own a gen 1 iPad, loved, loved playing games on it. Even at home although I have a PS3, the iPad was what I grabbed when I wanted to play a game (quite often, not always).
Now I have the mini, it's all the iPad gen 1 was with games, and so much more. The games I used to enjoy are just as enjoyable on the mini, but additionally, the size of the mini is for me ideal, so some of the games are just that much more manageable. I can hold the device in one hand (easily) and touch/play with the other, or I can use both hands and touch all areas of the screen.
While I would never say a full sized tablet is wrong, especially for game play, for me the mini is the bee's knees!