If we made "recklessly shooting into the woods" illegal, hunting enthusiasts and the NRA would be up in arms.
Besides which, there's no evidence such a thing happened with the drone - all we can tell from the video is that the drone was firing a pistol in the woods. It could perfectly well have been firing into the side of dirt hill that was off-camera. Maybe even someone's safely designed target shooting range.
I think there's a difference between "shooting into the woods" and "recklessly shooting into the woods."
If I own 100 acres of private land that I have marked as private, and I go into the middle of it and shoot away knowing full well that there's nearly no chance that a bystander will stop the round instead of a hill or tree, that's "shooting into the woods."
If I go into a public space of forest where I don't know who may be around, or where they may be, then that's "recklessly shooting into the woods."
The same logic applies to places where mountain biking is barred during hunting season on certain days...there's a recognition that there will be people with firearms who will likely shoot at targets that move at inhuman speed at the drop of a hat, and so there are rules to limit the risk to people as a result. (I only know of this situation because of recent mountain biking in Pennsylvania, in an area where this holds true for a lot of great trails.)
You're absolutely right, though; there's nothing that indicates (unless the video has GPS metadata) where this happened, in what direction the rounds traveled, or where they might have ended up. And in the absence of probable cause that something was wrong about one of those factors, I wouldn't think he should be charged with reckless use of a firearm. And certainly in the absence of proof of the same, he shouldn't be convicted.
What I see is someone looking at the video, and imagining the potential harm if someone used the same technology in a really bad way. There's a bit of knee-jerking here to go after the guy they can go after instead of the bad guy they can imagine (but who doesn't exist...yet). I think this guy was kind of dumb to post a video like this, even though I think he should have the right to do so without negative consequences.