We know that the jaw bone can grow throughout adulthood via endochondral ossification of the articular cartilage. This may be why we see people with acromegaly have very large jaws. The reason that the jaw bone continues to grow at the articulations and the other bones don’t is because the jaw bone is less constrained by ligaments and is very moveable so the stress that the articular cartilage undergoes is enough to induce articular cartilage endochondral ossification and also the lateral pterygoid muscle is attached to the articular cartilage directly so if you stimulate the lateral pterygoid muscle in any way either via forced mouth opening or a bite jumping appliance you get the pull with if it’s sufficient results in articular cartilage endochondral ossification. You can literally see this in the histological slides in the above link. The problem is that this likely occurs very slowly unless cell turnover is highly accelerated like via HGH which occurs in acromegaly.
So there are two problems why we don’t see more development of the jaw in normal individuals:
1) The lateral pterygoid muscle isn’t stimulated enough because they don’t chew strong enough food or they don’t practice “mewing“(which does stimulate the lateral pterygoid muscle by the way and it’s slightly dynamic as while you are moving around your muscles have to adjust to keep your tongue to the roof of the mouth). And it’s possible that normal strength training exercise will also stimulate lateral pterygoid development. An exercise like the deadlift pulls on every muscle in the body but that pull won’t be as strong as if you train the lateral pterygoid muscle directly.
2) articular cartilage endochondral ossification is very slow unless again it’s accelerated by HGH.
One problem with the device is that you can’t really do anything else while using it. You might as well just pull on your fingers directly. The other problem I see is that the device doesn’t really look like it would stretch the articular cartilage directly. It looks like it would mostly stretch the skin.
We’d have to really look at the pull to see if it was pulling directly at the articular cartilage. The best bet in my mind to provide a sufficient stretch on the articular cartilage would be a twisting or bending motion of the joint. This would get around the issue of the ligaments limiting the potential stretch. The issue would be potential cartilage damage from improper joint movement. Also based on joint mechanics it may still not stretch the articular cartilage in a sufficient manner.