Thank you for pointing us to this solution. We had the same question.
We’ve had some trouble to figure out why there remained a white frame around the background video. After a while we found out that one has to take care of the general settings in GP customizer for container margins. I just wanted to add this experience.
And there is a related question:
Unfortunately the video does not auto-play on mobile (iOS Safari / others not tested). Do you know how to force it to play?