Sync'ing games to iPod with iTunes 7.5

Do you still lose all the games you sync'd from one computer if you want to sync a game onto your iPod with another computer?

I bought all my iPod games on a computer that no longer works, and I want to play Phase. I won't buy it, however, if I am forced to repurchase all the other games I have already just so I can keep playing them.

Here's what I did when I started syncing with my Mac. I had originally bought Ms. Pac-Man and Tetris on a Windows PC. Since I had the games on my iPod classic already, I just used iTunes, connected my iPod to my Mac, and clicked on transfer purchases. This transfered my purchased games to the Mac and so when I started syncing with the Mac, the games remaned on the iPod. No need to rebuy them just because you want to switch computers.

Wow, I didn't even know that option was there. I feel like such an idiot. Thanks.