I'm not sure how anyone would know that a deer was being chased by dogs unless they were on his tail. In my experience, the deer always a good lead and you only know that dogs are pushing them because they show up minutes after seeking a deer come by briskly. If that's a law, I'm certain its to prevent the utilization of dogs in a hunt, not hunters who kill a deer being chased by wild dogs.

Anyway, I shoot them when I repeatedly see them chasing on my land and always will. I love my dogs dearly and take dog ownership seriously. If I let my dogs run wild on other peoples property and someone shot them I would only be angry at myself.

"The use of dogs in taking or attempting
to take deer is prohibited. Taking or attempting
to take deer being pursued by
dog, or dogs, is prohibited."

It says nothing about who owns the dogs or who owns the land.