The page in your example isn't full-screen, nor is it even full-viewport, it's a small video with a black background that blends into the page's black background. If you can get away with doing that, that will work.
If you care, you will never be able to auto-play an HTML5 video intro on iPad, because iOS inhibits autoload
and autoplay
unless they are triggered by a finger touching the screen. But then again, it can't play Flash anyway.
If you want an HTML5 video to be full-viewport, for, say, a 16:9 video viewed in a 4:3 monitor, you will make the video full-height and lose the sides of the video. Similarly for the reverse case. This will maintain the video's aspect ratio with the caveat that you lose part of the video content to hidden overflow.
If you don't care about aspect ratio, you can make the video height: 100%
and width: 100%
, as @coder suggests.
For this reason, it's probably easier to go with what they did on your example site, and make the video blend into the background.