While this study is small and it would be unwise to draw too many conclusions, it appears that perhaps interaction with an animal may trigger the mechanisms responsible for the concept of "theory-of-mind" in these children, or the ability to take the other's perspective even if "the other" is an animal. It appears that a new pet may make the child want to work at negotiating a relationship with that animal, exercising the muscles responsible for noticing and attending to the cues in the behaviors of others that signify the other's needs, such as when the animal wants to be played with, fed, or petted.
Interestingly, the study did not find any differences between those kids who had a pet since birth and those who never had a pet on how social behaviors progressed over time. Perhaps it is the novelty of this new being that may trigger a wish from the child to learn more about it and hence provides more intrinsic motivation to relate to it. Or maybe in the instances when the pet precedes the child, the pet is trained to behave in a certain way with the new baby, but when the animal is introduced when the child is older, the two are forced to negotiate their own unique relationship. Or it may simply be that this new thing is soft and fuzzy, and the only way for the child to get the novel sensory good stuff from this creature (i.e., petting, warmth, cuddling--rush of oxytocin), without the bad stuff (i.e.,biting or scratching--pain) is to learn the pet's behavioral and perhaps non-behavioral cues.