It's not unethical to shoot at a moving animal inside 200 yards. Flat out running at 200 sure, but walking, or trotting along - not an issue at all. Why would it be unethical? If can't hit a walking deer in the lungs at 200 yards, got no reason to be out there.
I'm not a long range shooter - don't have the opportunity, furthest shooting range I have local is 250 yards. I can shoot about an inch at that distance if me, the gun & ammo are up to it that day. That's about as good as I get with my equipment, amount of time, money, and energy used.
That makes at least point. If you are competent for the shot you take, then its ethical... if you aren't competent, then don't go out or limit the shots you take.
I shot my cow bison on a trot at 150ish. It was a simple clean shot. Three other hunters took shots and missed or didn't wound them at the same range on a trot broadside. The only other two hunters to take a cow out of the herd got them standing broadside. A couple hunters didn't take shots, ethical decision for them.
There were four different kinds of hunters, IMO there...