I don't know much about HDMI, but couldn't I just run the video/movie in fullscreen and then capture the output from the HDMI and save the raw output to a disk?
But the problem is that those are very high-speed signals(1920x1080 24bpp at 60FPS is around 350MB/s+) that require suitable hardware to capture, basically uncompressed video, and recompression would introduce more artifacts than the original. That's why pirates don't usually go this route; the result is only slightly better than pointing a good camera at the screen.