SKNET MonsterX Live device

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Input: 1080p60 (and lower) over HDMI (+ audio line-in)
Output: 720p (or 480p) MJPEG AVI over USB

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ID:	15008 (JP)

Google translation of the three main pages: (¥14,544 JPY):

For some reason all of their example footage is of recording a concert rather than video game playing. But if you kids can convince your parents to spend the money and import this from Japan, it could be a nice solution to your woes of hooking up your Xbox 360 to record on your laptop.

Expect to spend around $250-280 USD all-in with brokerage, import, middleman, shipping etc. fees. I'm guessing.