You play iPad games on an iPad -- not PC games or Mac games.
Some games have been ported to iPad so you can play the iPad version.
Also, you buy the games through the iPad's App store not Big Fish.
On a PC or Mac, purchases for iPad will show up under iTunes, but on the iPad itself they are under "App Store."
You can read about the Big Fish games for iPad on the Big Fish site
http://www.bigfishgames.com/mobile-games/ios-games/However if you want to try or buy, Big Fish will forward you to iTunes.
You don't really have the same guarantees as with the games for PC and Mac that Big Fish sells directly. If something goes wrong with a game, Big Fish can't give you a credit for another iPad game, though they may give you a credit for a PC or Mac game.