Frisbee is definitely out. I had a rat as a kid and think they make great pets. But you have to be careful with them because they are fragile, so make sure they don't fall off of anything (a table or your shoulder) or get dropped. They also get pneumonia easily, so keep them away from open water (no swimming in the tub, for instance).
Instead of teaching him games, maybe you would have just as much fun teaching him tricks. He can learn to do things that come natural to rats, but since he'll do them on your command, it looks very clever. Below are some web sites that give tips on tricks you can teach your rat. Just use a lot of patience, never discipline your rat, just give him rewards when he finally gets the idea what you want. You can find lots more tricks to teach your rat by searching on "rat tricks".
