In fact, the video (and Luna) uses neither GNOME nor compiz. We use our own window manager called "Gala"[1] (it is based on the same library that gnome's is) in our own desktop environment called "Pantheon"[2].

[1] http://elementaryos.org/journal/meet-gala-window-manager

[2] (I couldn't find an elementary journal article explicitly about this, but here's one from the Gentoo wiki): http://wiki.gentoo.org/wiki/Pantheon