There are actually a lot of games which are compatible with your older device which runs iOS 3.1.3. You just need a tool to separate them from the incompatible apps.
Here is my favorite solution:
iOSSearch - search the iTunes store for compatible apps.
And here are some things other people have suggested:
Vintapps 3.1.3 - paid app.
Apple Club - filter apps by iOS version.
Discussion post by msgarmar - technique to sort apps by date.