This page shows how to create the embed code for any Facebook video to embed them in external websites.
Is there a way to start the playback automatically on page lo
waitforclick
Indicates whether to autoplay the Flash object (false) when allowed. false does not work in profiles for security and aesthetic reasons, except after an AJAX call. Default value is true
https://developers.facebook.com/docs/reference/fbml/swf/
U have to change the the example code from the bottom to the the facebook video, like in your provided link explained.
Didnt tried it, but maybe it helps
regards