All in One SEO plugin is setting your FaceBook open graph meta tags. For Facebook to “see” your video, you need to set video meta tags:
<meta property="og:video" content="http://example.com/movie.swf" />
<meta property="og:video:secure_url" content="https://secure.example.com/movie.swf" />
<meta property="og:video:type" content="application/x-shockwave-flash" />
<meta property="og:video:width" content="400" />
<meta property="og:video:height" content="300" />
Whether or not this is possible with that plugin or will have to be done manually, I can’t tell you.
EDIT- on second glance I missed the closing comment for the plugin, it appears the tags are being inserted by something else.