If you check the HTML in this page, you will see that the YouTube URL that the forum software is writing out contains a blank "list=" parameter. If you remove this parameter, the embed works fine.
Edit: it looks like this problem has sprung up out of the blue, it has been reported elsewhere. It sounds like an easy fix, you need to edit the template
Code:
_media_site_embed_youtube
and remove the
Code:
&list={$list}
part of the src of the iframe. For whatever reason, I'm assuming the software has decided to stop writing in the value for the parameter.