The claim here is that it's axiomatically asserted as okay to eat animals if it's for some specific purpose, (generally food). For instance, one is using the animal to feed oneself, so it's not just for entertainment. A more extreme case is that, in a desert island scenario, one is using the animal for sustenance, so it is justified there as well.
When faced with a grocery store aisle and having a choice between sticking a bag of imitation or real chicken in one's basket, barring unusual scenarios, the choice of real chicken is based purely on taste alone. Hence, it's purely for entertainment, in moral terms.
If one is faced with either starvation or eating an animal, then it is in fact appropriate to say that the animal is eaten "for sustenance". But in the scenario when one has the choice between more than one option of what to eat, either one can be eaten "for sustenance", so it isn't fair to say that it's making the difference when picking one over the other. The only real difference between those options is taste.
So the fact that one is eating an animal doesn't mean that "the animal is killed to sustain me". That's an arbitrary dividing line within the category of entertainment. Would it matter if I killed cats - or, say, infants - for entertainment in the form of food? It shouldn't be in moral terms. There's no significant moral difference between liking the way a pig sounds when dying and liking the way it tastes once dead.
Unless you can demonstrate it is necessary it doesn't change the moral calculus significantly.