In a rural area, I'd think the most he could be charged with is property damage, but a drone hovering at a low altitude over private property must in my view (not sure about legally) be considered trespassing, which would be a mitigating factor. If a robot with a camera rolled or walked onto your property, what are your rights? The same should apply to flying drones, at least below a certain altitude.
If he was using birdshot, there would be no risk to anyone past a few hundred feet. If there was a risk, trap/skeet would not be possible in most of the places where you can shoot it.
This is of particular personal interest to me, because I fly gliders and sometimes we end up making emergency landings on other people's property when the weather doesn't quite cooperate with us.
My understanding of the law there is that I'm liable (and covered by my insurance) for any damage I cause to their property in the course of landing and retrieval, but the property owner can't stop me from retrieving my aircraft, and can't intentionally damage it.
Now, the fact that it's technically an emergency landing does change things a bit, for example my actions aren't a crime the way normal trespass would be. But I don't believe it changes the property owner's rights and responsibilities.
I had a neighbor who was shooting his assault rifle into the ground in his back yard (a typical suburban neighborhood). After a few shots, the police were called, and they showed up with an entire SWAT team. Confiscated his weapons and threw him in jail for a couple days. He wasn't waving it around, and wasn't threatening anyone. It was only 3 rounds, actually, but it was enough.
Similarly, if someone is flying a kite and it is over your backyard and you shoot the kite with a bb gun enough to bring it down, what would the police do? Is a kite any different than a drone, legally speaking?