Neko

A kind of proto-Catz, Neko places an animated cat in a window on your desktop. While this is more of a software toy than a "game" per se, certainly you play with it: Neko chases the mouse cursor, scratching at the window borders if they get in the way. Leave the mouse idle for long enough and Neko will groom and go to sleep; move it suddenly and Neko will awaken, to resume the chase!