It looks as though that product allows you to record video, not interact with or play it from your MacBook. I do not think it will allow you to control you Xbox from the MacBook.
You want a "TV tuner" type product. Many of the TV tuners only have a connector for the antenna, so you'll want to find one that has a composite video input or S-video input. (Composite video, the kind for hooking up a cheap VCR, etc.) Without the composite video input, you'd need an RF modulator, which is getting harder to find nowdays and would give you very poor video quality anyway.
I haven't seen any USB TV tuners that have
component video input. Component video is higher quality than composite video, but you may have to settle for composite or S-video.
I read in a magazine about the Elgato EyeTV Hybrid, which was recommended for playing console games on the Mac. Unlike other similar products, the EyeTV Hybrid does not encode video before sending it to the Mac. This means there is only a few milliseconds of delay, meaning no appreciable lag.
If you decide to get the device, I found it in the Apple store for $149.95 (Free shipping). It comes with an adaptor to allow composite RCA and S-Video to be connected (no support for HDTV, however).
I hope that this helps you to make a decision on what to do.