This is an accepted solution.
The issue with the theme, in this case, is that the source code includes a rule to support video play-back only past a certain screen width threshold. If the screen of the mobile device is narrower than that minimum size, then the video does not play, and instead, you get your chosen thumbnail displayed. I believe the set minimum width was 749 points. Tablets would pass the threshold, phones in vertical view would not. They do if you rotate your screen, but that might as well distort the page's proportions. We've just looked at this and I can't give you any code snippets to fix it, but if you know which parts of the source code to look at, you might be able to figure out how to bypass or rewrite the rule.