How to copy pre-installed games from a 5th gen classic to a click-wheel nano?

I have an older 5th Gen Classic iPod (80gb) and my sister has a slighter newer iPod Nano (not sure on the specifics but they're both click-wheel).

Is there any way for me to copy my pre-installed click-wheel games (Brick, Solitaire, etc) to her nano (which only has Tetris)? And now that we can't buy new games, we're both at a loss for what to do 😟

We'd like to share games but I can't figure out where my pre-installed games are in order to transfer them, and there doesn't seem to be any way for me to backup the games on my iPod through iTunes 😟