According to a meta.stackexchange answer, YouTube/HTML-5 video embedding has been allowed for a few years now.
All Stack Exchange sites that have either YouTube or SoundCloud embedding enabled now use the respective IFRAME embeds. In light of recent flash-related happenings, we have also re-rendered all affected posts, which means that even old questions and answers that contain an embedded video will now use the HTML5 player.
Bye bye, Flash.
I just tried to embed a YouTube video into an answer of mine, and the video does not show up. Per the above quote, does TGO have videos enabled?