'Humane Kill' would imply killing as humanely as practically possible. This would distinguish it from a 'sadistic kill' for example. I think that the point is that you can kill something in such a way as to minimise its pain (as far as is practical), and this would be decribed as humane, (with humanity) to kill something in a way in which you ensured it suffered the most pain before it died (to take the opposite extreme) would be a 'sadistic kill'.
Despite what some people may think, possibly yourself amongst them, we do not generally hunt because we enjoy the act of killing per se, if that was our goal then it would be far more economical to buy rabbits and hamsters from pet shops and torture them to death, than to hunt animals in the wild.
Obviously we do not all achieve the most humane kill possible with every shot, but most of us always do everything we reasonably can to ensure that we are as humane as possible.
Hope that clears things up for you a little.
Alex