What would you recommend me to record videos while playing Xbox360
The hyperdeck shuttle is a small, lightweight and easy-to-use field recorder. The downside it just works with expensive SSD volumes. 

A possible alternative could be the Atomos Ninja. - Pros: Runs with SSD, but also with cheap and capacious 2.5-inch-HDDs. Built-in Touch-LCD-screen. Double battery connectors. The drives and batteries are hot-swapable. Cons: It's weight and it's size.