can you put games on the small jump drives and use them on another computer?

Depends on the game. If the game is one that keeps all its files in a single directory, then it would work. If the game as to add files to windows/system32 (such as a dll) and add entries to the registry, then it would not work.

You could, however, include the install file on the jump drive, install it on the computer, play, and remove the game from the computer when done.

Voltron USB Flash Drive (Collectible action figure)