After "mobile friendly" update, MP4 videos do not play on iPhones

Apparently my login timed out while I was composing this post, so I apologize if this is the second time it's appearing. I also tried doing a search for other reports of this problem and I did not come up with any results that were pertinent upon reading the first few posts, so I apologize if I didn't look hard enough and am reposting about a known issue.

I have two different web sites using the Atahualpa theme. Both are using the most current version and have the recommended patches applied. After following Juggledad's directions for making Atahualpa WP sites pass Google's "mobile friendly" test people have been pointing out to me that MP4 videos do not play on iPhones. Because I don't own any Apple devices I asked some friends to test the video and you can read the results below. The problem seems to occur regardless of which version of the iPhone was being used, and also regardless of which version of iOS.

Site A: This site has had the "mobile friendly" changes applied. If you have an iPhone and try to view any of the videos on the page below, they will not work. (Take the first one, "What If..." as an example.)
http://scs-matters.com/video/

Site B: I have not yet applied the "mobile friendly" changes to this site. I've put the exact same "What If..." video on the page below, and it plays just fine on iPhones.
http://operapaintings.com/video-test-page/

Does anyone have any idea what might be causing this, and more importantly how I could fix it?