I don't understand the head shake either, I would think it would be hard to keep and nice even contact with the bridle with all that head movement. Don't the MFT's do a head bob too. My breed, the Peruvian, carries a quiet head. Interesting how different variations on a 4 beat gait can have such different head carriages.
The head bob up and down is supposed to be like us, using our arms in a power walk...sort of a bad analogy but gets tossed around a lot. I don't look for a huge head nod in a tw, but do look for it to a degree. You don't want to see a side to side head movement as that'll be a sure fired way to tell the horse is pacing.
The paso breeds have zero head movement. It's a bit easier to ride in that your hands stay pretty still, it gives the horse a straight line from your hands to the bit to walk through, and that's what the paso folks are looking for, all straight lines and zero bend.
For me, I'm not overly impressed with this ride. I like the horse well enough, lot's of tallent there, imho, but I'm not liking the rider. He doesn't have quiet hands, he's widening the reins and adjusting a lot. To me, it looks like he's chasing this poor horse around the arena. The fw and rw can really move you back and forth in the saddle, they con't call it a camel walk for nothing, but to my eye, it looks forced on his part. He's not following the natural movement of the horse, he's using his whole body to push that horse forward and to me, that's much more distracting than the head bob. Not only is he jamming his pelvis back and forth, you can see it right up his back and into his neck in some places which I'm sure doesn't feel good on the horses' back.
I'd think this was a young horse in training and again, like the horse a lot. I'd just like to see him quit bumping his legs and being start being a bit softer in his aides. Any one else see this??