In many cases, I have observed that an emotional connection with another animal is enough to prevent hunting of either just the animal itself or in some cases the entire species. In a more extreme example I've known chickens to run amok and play with dogs like they were one of their own.
And not just dogs. I have trained cats to become friendly to individual rats (I think instinct is too strong), and I have seen some species express either preference or disdain for other species. My personal analysis is that this has more to do with social and emotional conditioning, a true recognition of another animal as "friendly" despite not offering a symbiotic relationship, rather than directly as a result of behavioral conditioning with positive/negative stimulus.
I think a better indicator of the difference between us and pets is that we keep pets, and further, that we sometimes keep pets purely for emotional benefits. Incidences of non-humans keeping other animals as pets is extremely rare and seemingly limited to primates. [0] I think that says a lot about our psychology. But it's a little pointless to debate about whether other mammals experience meaningful emotions. They do. Meaningful emotions are actionable. That's why our emotions seem meaningful.
[0] https://bioone.org/journals/Neotropical-Primates/volume-13/i...