My point with the pic of the deer that my son shot is that sometimes they don't flop at all and sometimes they do. I think it has more to do with what the projectile damages internally than the blanket statement that "all animals shot in the brain flop". I've seen rabbits in that I've head shot "running in place" on their side or back with devastating damage to the head. I've also seen them drop and not move at all. As far as muscle movements after taking game.....last fall I field dressed a doe my friend shot through both lungs. It was his first deer so I helped him out. When had already opened up the cavity and were in the process of splitting the pelvis to get the lower tract free and the deers hind leg muscles were "rippling". Not twitching and actually moving the legs at all but kind of tensing up an causing a rippling effect in the muscle. Deer was clearly "expired" and had been for 15 to 20 minutes when we noticed it.I don't know about the video's authenticity, but as to the question of "flopping around" ...
As I understand it, instinctive movements, like running motions even though the animal is down or movements that might be designed to disengage from the grasp of a predator, occur because of disinhibition. That is to say, the brain normally inhibits instinctive movements, and when you suddenly take the brain offline while the rest of the CNS is still functioning, the lower parts of the CNS just cut loose. That's the explanation of it that stuck in my brain, for better or for worse. Perhaps if certain parts of the brain are left intact, the instinctive movements are still inhibited during the brief window during which they could otherwise occur. Maybe this guy scrambled his cerebral cortex, but the lower part of the brain was still functioning well enough to inhibit other movements.
Death of the body is a curious thing. There clearly can me movement of muscles well after actual death.