The following website: http://www.themedept.com/demo/getleads/agency.html
Shows a looping video: http://www.themedept.com/demo/getleads/images/video/video.mp4
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I have the same issue (Chrome 54.0.2840.99 m) but I found that it at least works in an incognito session.
It seems that Chrome Dev Tools is not respecting the "Disable cache" setting for videos.
The same problem in Mozilla FireFox. You can use Private Window in FireFox for video src request. Or Incognito in Chrome.
I used MS edge Version 86.0.622.48 (I am on macOS Mojave) and it works just fine! For sending for those who have issues with Chrome and Firefox!