I planning to get an IOS device but then
when i search the iTune store some of the games compatibility only list for
Requires iOS 5.1 or later. Compatible with iPhone, iPad, and iPod touch. This app is optimized for iPhone 5.
I don't see Ipad Mini and Ipad Air in the list. So does this means two of this device cannot play the game?

“iPad” includes all models (iPad 1,2,3,4 / iPad Air / iPad mini 1,2) unless the App Store product description specifically mentions that a particular device is not supported (e.g. there are some games that can’t be played on iPad 1 or iPad mini, usually due to hardware limitations or incompatible display resolution). Always read the product description, and you're good to go.