The MacBook Air fulfills most of the minimum requirements, but for the best experience, you need a 1GB dedicated graphics card, and a 3Ghz multi-core processor, which are both not present on the MacBook Air. As for Mac App Store games, it can certainly handle games like Angry Birds and Rail Maze, but for games like Call of Duty 4, you could play it in low settings, but don't expect it to play silky-smooth when turned up to high.
MacBook Air is not a good choice for gaming, it is more like a laptop for people who just do web browsing and email. If you really want to game, get the 15 MacBook Pro or iMac, or even better, a gaming PC.