Nice shooting indeed. It’s extremely difficult to shoot a dog charging at you in the back of his head.
A few years ago, a dang dog was running deer through one of my tobacco fields, instead of shooting the dog I shot in front of him to run him off. Killed him dead, when I went down where he was I noticed I had hit a rock, a chip of rock hit the dog in the head and killed him. But in this case, I would say he was putting the dog out of pain.