Just to point this out. You can see his club face at the top is nearly the same angle as his left hand. This is due to his grip, but it tells me his left forearm has rotated 90 degrees from the initial set up. If it didn't rotate the back of the left hand would be facing the camera. There is a natural rotation in the forearm in the golf swing. So it is not a square to square motion. The club face never stays square to the swing plane. He might FEEL like his clubface stays square, but it doesn't.
FWIW, I'm pretty sure the whole square to square concept refers to waist high to waist high? Can @samgouldengolf elaborate?
I'll come clean and admit I only watch the first quarter of the video, my damn office phone keeps ringing, really interferes with my golf study.