I shot off-hand at a running deer at 100 yards when I was young. I hit it in the jaw. If I hadn't calmed down, and sat down, and made my second shot count, he would have died a lingering death. I feel pretty confident shooting at a running animal at 50 or 60 yards. Beyond that, I don't even think about it. I have found that an ELK brand deer call will often stop a running mule deer. A cow call will often get elk to run towards you after a shot. Shooting at a running antelope at 200 yards can result in the antelope behind it being shot. Don't ask how I know.
A former friend gut shot a javelina, and we were following a good blood trail. He saw two more, and took another shot with his bow. Fortunately, he missed, and we harvested the wounded pig. He was never invited to hunt with me again.
Fortunately, the chances of him hitting a running moose at that distance are small. I double checked the math, and a 180 gr. bullet starting at 2550 from a .308 takes at least 1/2 a second to get there. A moose can run 35 mph (51 feet/sec) so that's 25 feet or so. Add to that the fact that you really don't know how fast he is running, and the variables are immense. Carlos Hathcock maybe. He claimed to have hit the fork of a moving bicycle pedaled by a Vietnamese kid moving guns .