Connecting Skype with Facebook is not (yet) supported in the latest version of Skype for Linux. The video you posted shows using Skype on Microsoft Windows.
Unfortunately, Facebook does not support video calling on Ubuntu yet, as explained on the Facebook Help Center. They haven't developed their plugin yet.
However, video calling (popularly known as Hangouts) works on Google+, for example (after installing a plugin). If you are curious in upcoming technologies, you also can take a look at WebRTC.
open pidigin accounts and edit the facebook account to the following:
Protocol: XMPP
Username: xyz (This might not be the username that you enter at facebook login page - But the one which you see on your timeline link - https://www.facebook.com/xyz)
Domain: chat.facebook.com
Resource: Pidgin (this is what is missing most of the time)
Best Answer
Connecting Skype with Facebook is not (yet) supported in the latest version of Skype for Linux. The video you posted shows using Skype on Microsoft Windows.
Proof : 12/1/2013