I watched again and there definitely is another piece missing from the puzzle, at about the two o’clock position, at the end of the trick. As he dismisses the audience member, the magician looks directly at it and appears to hesitate for a second (maybe wondering what to do). When the camera cuts back to him after an audience shot, the piece has been put back. I’m wondering if he picked up the piece and put it back, which would be obvious to everyone, or if the producers did another take. But then, why wouldn’t they redo the whole trick so we never see the piece missing?
The piece did come from the spot where his watch or bracelet was toward the end of the trick.
There has to be something he manipulated when taking the cloth off. I didn’t see anything obvious with touching puzzle itself, but watch his left hand as he’s removing the cloth. Both hands are on the top of the frame, but as he removes the cloth his left hand slides to the left as if he is manipulating something behind the puzzle. It’s an odd and unnecessary movement for just removing the cloth, and he directs attention to the audience member with some comment as he does it.