Ipod touch and games

I was wondering if the games you buy from the Itunes store play on the Ipod touch? I wanted to buy sonic, pacman, tetris, and soduku. Will these games play?

I was a little confused because in the game section of the Itunes store it said that the all 5th gen Ipods play the games, but I was not sure if Ipod touch falls into this category.

 

Thanks for the help, but that's dissapointing news.