Responsive Website Video
Playing video on a responsive site is tricly because the file needs to be prevented from downloading on page load, a poster image is required and the visitor should be given the choice of an SD and an HD video file.
Autoplay
I think most web designers are now familiar with the fact that video will NOY autoplay on Safari for desktop and mobile unless there is no soundtrack or the sound is muted.
Background
Playing a video in the browser background is a complete disaster for visitors using mobile phones since they need to download a very big video fil ewhether they want to watch it or not.