I tried to insert a local video with autoplay. It didn't work with Firefox or Chrome. I found out that "muted" has to be activated as well.
But when I click on "Mute" in the Media Options, no muted is set in the video tag. This seams to be a bug.
I added by hand "muted" and my video start as expected!
<video src="https://www.joomlacontenteditor.net/images/video/sportstudio-nippon-kampfkunst.mp4" poster="/images/video/start-bild-sportstudio-nippon-2.jpg" autoplay="autoplay" loop="loop" muted="" controls="controls" width="1280" height="720" id="vid" type="video/mp4"></video>