I'm not sure the guitar in the still shots and the guitar in the video in the OP are the same instrument.
Check out these captures I made from the video:
While there is too much motion blur to really make out the knobs, this guitar has what looks like a Maestro-type tailpiece in the first pic. Les Paul is in the process of picking up the guitar in this shot, so there is some motion blur, but you can also make out a long bar extending from the tailpiece, just over the corner of the pickguard.
In the second still image, the bar is much clearer. It has a curve to it and extends from the tailpiece itself to just over the corner of the pickguard, as in the first pic. There are other close-up shots in the video where this bar is apparent.
I've looked for other images of this guitar and can't find them.
However, here is another video with another guitar. In this video, it is unmistakably clear. The guitar has two pickups, but only two knobs, AND the guitar output jack is on the face of the guitar, not on the side.