If you were to "record" it the way you're suggesting, you'll lose significant picture quality. Also, it is a video file. And it is scripted to play at a certain point within the demo.
The movies are not being rendered by the game's engine or anything like that, they're pre-rendered videos. The point is that you still have all of that information on screen, and it's a lot of data to process. The program that creates the videos is where they would export from, and that original video file would be massive. They could compress that video, but then they would lose the video quality. (Even with a lossless compressor, the size is still huge.)
HD footage typically works out to be about 1 minute of HD video = 1 GB of data. And that's talking about a handheld, home video camera. If you create CG images, with tons of special effects, and export out as HD video, you're file sizes are going to be massive.
Point being, they clearly did all the compressing they could to the videos, and that's about as small as they're going to get without sacrificing video quality.
Also, most movies these days still shoot on film. So an HD-DVD video was not actually shot on HD footage necessarily. It was just converted to HD for the DVD version.
It's starting to become more popular, but it's still quite recent. Michael Mann is one of the folks who have started shooting HD Hollywood status films. i.e. "Collateral" and "Miami Vice".