I'll take the opposite stance and state the police officers were correct to take the course of action they did.
Human lives, imo, are more important than animal lives, (mostly) and a stray dog running amok on a motorway could easily have caused loss of life. One must also question why a domestic pet was being allowed to run loose without a lead, chances are the dog had an irresponsible owner or was a stray.
People, imo, get too emotional about animals, sure, they're cute, some are good companions, but we are top of the food chain so lets look after ourselves.
Nobody bats an eyelid about thousands of animals slaughtered daily for their dinner plate by having their throat cut whilst still fully conscious so the death of one dog pales in comparison.
My deceased father in law was raised on a farm and they used dogs to help work the farm. When the dog came beyond use it was put down, with a shotgun. FIL said to me 'Sure, we got attached to the dogs, became fond of them, but at the end of the day they were just tools'.
I deplore the unnecessary death of any living creature and would also consider myself an animal lover. I detest hunting (unless it's strictly for food) and tbh I find the antics of those 'big game hunters' in Africa more obscene than the putting down of one dog.
There, said my bit, now where's my crash helmet...