No, but kneecapping this guy because he maliciously and needlessly shot a domesticated animal isn't over the top.
Yes it is over the top. Completely and violently over the top. It's a nonsentient, instinctual, and possibly packish dog, that the officer believed was killing wild game. In your (and all the anthropomorphizers) opinion this dog somehow has human qualities and characteristics, which if you want to believe it is fine, but the minute you expect me to also believe your completely irrational and illogical behavior, your game must end and reality needs to step in.
All dogs regardless of owner and their place in your household are nothing but animals, and just like the deer (which noone seems upset about) it's life is not as valuable as a humans and in the eyes of the law and society it's nothing but property. If property gets out of line or is a public nuisance it's condemned. The officer that is responsible for this decision, determined that this animal was a public nuisance and took the appropriate action to remedy the problem.
Example:
My senior year of high school, we developed a huge problem with feral dogs. These were even worse than wolves or coyotes because they had no fear of humans and would enter human areas and even approach humans even when well fed. They started with taking sheep. Then they got a couple of calves, and eventually they started killing other pets, including we thought our neighbors two german sheperds because the amount of blood and fur that we found.
I had been actively tracking the pack for a month or so while checking cattle, so when the sheriff and game warden set up a group to destroy them I got to go along. It was not a happy trip. No one enjoys destroying animals, and we really weren't looking forward to the close to 15 that we knew we were going to have to kill.
We found them. In observing, I noticed that the neighbors two dogs had not been killed by the pack, but in fact had joined. We set up at about 200 yards and started shooting. Some of the dogs obviously scented us and rather than running away, they started running towards us. Their tails were up and wagging, their mouths open, basically all the signs that they were happy to see us and were non aggressive. We killed them all.
I know for a fact that had we not shot the dogs, I could have easily grabbed the two neighbor's dogs and taken them back to him, they probably would have come willingly and definitely nonagressively, because they knew me and they behaved around me just like they did around him. However, that's not the point.
These dogs like all dogs have a natural aggressive and violent instinct. In controlled environments with well established orders of dominance and control, any dog can be trusted, but outside that environment, the natural instincts are closer to the surface and depending on the breed, the dog, and the training, they may take control should the situation push the dog far enough outside of the dog's comfort zone and when those natural instincts take over, you don't have a dog, or a pet, or something that you treat like a family member, you have a wild animal that's scared, capable of great violence, and unpredictable.
