I think it "just works" if you (a) post a YouTube link into a post using the desktop editor, or (b) post using the mobile editor BUT you have to use the link tool button in the toolbar to insert the link.

Test:
(EDIT: yeah, I just pasted the bare link into my post on the desktop interface and it automatically embedded)

p.s. to the admins this is another thing that frequently trips people up in the mobile skin (you see posts with URLs that have not been linkified), ought to be a trivial change (how is it the desktop editor and mobile editor don't submit to the same backend handler?) and would improve the mobile experience a lot.