“No where in the article does it say anything about the dog chasing deer, and a dog that is still in the general vicinity of it’s owners isn’t off running deer to death even if it isn’t on a leash.”
Tell that to all the states that allow anyone with a firearm to shoot a dog if he suspects it was chasing deer......
I highly doubt that you are permitted to shoot a dog on the mere suspicion that the dog is chasing a deer. I suspect you might actually have to see a deer and a dog giving chase.
Otherwise, you're just shooting someone's pet, which will get you charged with a felony and get your right to own firearms permanently suspended, so I suggest that you are careful to make sure that you see a dog actively chasing a deer before you shoot it.
Suspects, no, suspects doesn't cut it, in fact a hunter shooting a dog because he "suspects" is likely to be dealing with both civil action and perhaps criminal charges. I've no doubt some states allow a hunter to shoot a dog chasing deer, but most states that's limited to the DNR or police. I'd be careful shooting dogs.