Are you suggesting that if he had claimed that he generally appreciates elks but not the ones he kills, would make more sense?
(I am a meat-eater, just pointing out something I find funny in such statements)
I believe we may each be using the word "appreciate" with subtly different definitions. I believe it's possible to appreciate aspects of a thing without necessarily collapsing them all into some sort of comparison of perceived total value. I think it's possible that someone who hunts for sustenance might also come to treat the activity as somewhat of a sport, or an art, and so come to appreciate aspects of the activity including the intelligent behaviours of the prey.