As far as I can tell there shouldn't be any reason the game can't be compatible with the first generation iPod touch. As long as there aren't any hardware limitations, we should be able to get this done for you. After all, we'd love for you to be able to play a game you've already purchased!

In the meantime, have you updated the firmware to 2.2? If you're still running the 1.x firmware, you should be able to update it to the 2.x, although Apple will charge you $10 for the upgrade.