There is something about intelligence that seems to carry a degree of... moral responsibility, somehow? Though in reality it's just an animal eating another animal, as ever.
In the end, I think a gazelle doesn’t look up at the lion that killed it by outrunning it and the snapping its neck and say “Ah well, got me fair and square!”
I know this is tangential to your point, but lions don't really hunt that way. They ambush, as they could never outrun a gazelle, and then they don't snap its neck unless unintentionally. They tend to just start eating it while it is still alive. It's quite brutal to watch.
Humane hunting is mostly something that only a rich old guy with his night vision goggles and sniper rifle can afford.
Even for farm animals, many cultures perform their sacrifice in ghastly ways.