If you go to 23:35 it shows fairly well where the first shot hit. Definitely very high through the spinous processes. As others have stated, a hit near the spinal cord can deliver enough shock to stun the animal, dropping it to the ground temporarily.
As far as the cause of the high hit, I wonder if they got an accurate range from their rangefinder. It might have ranged the ground behind the deer instead of the deer itself, giving a yardage reading that was too long.
The dancing around after the shot was definitely a douchebag move. How about stay on the gun to make sure of the kill, then film the dancing later if you feel like you need it for the video.
