yep. It's a training fork, not a running martingale. It is adjusted too tight.
In theory, a running martingale is supposed to only come into play when the horse raises his head too high. At other times, the line from hand to mouth should be unbroken. In reality, even in a running martingale adjusted properly, it's hard to maintain a straight line, since the horse moves his head up and down, and so you get time when the hand is contacting at one angle (in line with the forearm of the rider) and times when the contact is a downward pull, when the ring of the martingale breaks the straight line from hand to bit. I can imagine this feels really confusing and uncomfortable for the horse.
That training fork is doing the same thing, except that it's so tight that the horse can only achieve any relief from the downward pull by keep his head quite low.
He looked pretty uncomfortable, and it's a shame because when the rider eased up he put his head in a very nice position for a pleasure horse and is a real cute little guy.