Another phone on your account that purchased a game?
I haven't heard of a game in the AppStore that has a monthly fee associated with it. I would be calling ATT.
Any app you download from the App Store would have nothing to do with you monthly AT&T bill. The "Game" that's on the bill is not an App Store app. It's probably another game that a different phone on your plan downloaded for their phone.
As others have said there are no apps that are billed by at&t for the iPhone. Sounds like you need to call CC and ask them about it. Explain that you've got an iPhone and they'll most likely credit you.
Another phone on your account that purchased a game?
I haven't heard of a game in the AppStore that has a monthly fee associated with it. I would be calling ATT.