I just discovered an annoying behavior in iTunes 7 when attempting to sync a iPod game to an iPod. After downloading the game, when you sync your iPod you will see a messages with text similar to:
Some of the games in your iTunes library, including the game "Vortex", were not copied to the iPod "Paul's Vide iPod" because you are not authorized to play them on this computer.
It looks like the act of downloading the game does not automatically authorize the computer. You have to double click on the game in iTunes, (even though the documentation of iTunes states that the games are not playable in iTunes) to authorize the computer.