It's a distinction that makes a lot more sense in the proper context. Keith wasn't shooting varmints for recreation, he was shooting to protect his & his friends' livestock. Same general sort of rules apply to that as to self-defense. Make any hit you can under the circumstances--even a poor hit may be enough to achieve your goal of staying alive (self-defense) or preventing the loss of livestock (pest/varmint control).I never have understood the philosophy that only deer need to be killed quickly and humanely, whereas coyotes, bobcats, wolves and other critters, just deserve to be shot.
Most varmint hunters these days are hunting for recreation and under those circumstances, IMO, the hunter has the same obligation to administer a quick, clean kill as he would if he were shooting a game animal.