If your purchased games are now in iTunes, the next time you sync your iPod to iTunes, your game should move to the iPod. If you are using manually manage for your iPod content, then you would have to drag/drop the game from iTunes onto the iPod when the iPod appears in the source pane in iTunes. Post back if you have any more questions.
if you manage your ipod manually, you'll have to click on your ipod, go to games and then check the box next to the game you want on your ipod and click "sync selected games" and that should work.
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games on ipod
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