On occasion, a good-hearted person decides that the NAP applies to animals. What they usually mean by this is not that animals can be expected to accept it, of course, since almost no one is that divorced from reality.
What they mean is that if person A is harming an animal, then person B is entitled to use “defensive” force against person A, just as would be the case if person A were harming another human.
Obviously this cannot be true, because if it were, it would mean that anyone who interacts with any animal without the animal’s consent is guilty of a crime, as he would be if the animal were a human being.
This leads immediately to the conclusions that pet owners are slaveholders, meat-eaters are (at least) accessories to murder, and many other obviously ridiculous conclusions.
Again, of course it is not true that anyone who follows the NAP is a “good person”, or is entitled to have others deal with him voluntarily. If most people think that meat-eating is a terrible evil, then those people would be free in anarchy to shun meat eaters. But they would still not be free to use violence against them, as that would be a NAP violation.
But if you don’t accept the consequentialist reasoning above, then you should also consider that “argumentation ethics”, which logically proves the validity of the NAP, applies only to beings capable of reasoning. If a dolphin (for example) turns out to be able to discuss and agree to the NAP, then that dolphin would also be entitled to claim its protections.
So far, though, we have only us.