Hello,
as Justin Hunt explains in his article, the Moodle Mobile app only receives the HTML of the player, not the Javascript and CSS, that's why it doesn't work. The default way to embed videos in Moodle works because it's just an HTML5 player, with no Javascript. In case of Youtube videos, they work because they are inside an iframe, the main problem of this solution is that the video will only be seen if the user is online.
The video players should always rely on a HTML5 video player so if the JS isn't run the video will still be seen.
Cheers,
Dani