I think a big part of this would depend on whether the guy shot the dog because he really didn’t want it in his yard, or if he shot the dog, knowing it would affect the owners. Obviously, it would be very hard to prove the latter, but if it was, then he knew they would suffer a great loss.
Also we don’t know if the guy had reasonable control over his dog. Also were any warnings given about the dog being in the guy’s yard.
I live in a dog town and people here have pretty good control of their dogs but dogs do get loose on occasion. However we don’t shoot them at the first opportunity. If there’s a problem its taken up with the owners.