On your site, aside from the fact that the theme’s wrappers aren’t being applied, the video is also not embedded in the default way. It has some extra stuff around it. I remember seeing this same issue with someone else’s site once, but for the life of me, can’t figure out what it ended up being.
Do you have any plugins installed on your site that have anything to do with YouTube or embeds or videos? There has to be something else that is conflicting.