MP4s are universally recognized for all the major browsers so your MP4 itself might be corrupt. I go to the direct link of your MP4 and it doesn’t show video there so I want to say it’s something to do with your video.
Yes, I converted the webm version to mp4 and it seems to work now. I found an online converter at www.online-convert.com which seems to have done a good job and my mp4 is half the size.