Legally? I have no idea. Here I believe he could possibly be charged with destruction of property, unless zoning laws stated that he could not fire a shotgun. A shotgun fired upwards is very safe, the risk of anybody being hurt by a few birdshot coming down is minimal, so endangerment is only possibly from somebody being hit by the falling drone. And if that is a danger, what the heck is the drone doing flying over people anyway?
Morally? It seems to me that a majority of the drone pilots are douche bags, completely ignoring other peoples right to privacy and even safety. Just because it is possible to fly their drones anywhere does not mean it is a good idea. If somebody flies their drone into my property, collecting video footage, I believe I have the moral right to do something about it. It is no different from if they started racing around a RC car with a video camera in my backyard. Sure, I could call the police, but the police is unlikely to show up in time. And what is the police supposed to do about a drone hovering over my house? Waste time around until they find the pilot? This is a perfect example of when a well aimed shotgun shot will help improve how people behave. If they don't want their drones shot down, they can fly them over their own property.