The closest answer is zoomorphism, which is giving animal traits to non-animal subjects or objects, as in the sidewalk that "purrs."
There is an interesting issue bubbling under the surface of this question, though: how do we draw a line between animals and humans? Since the advent of Darwinism, humans have been understood to have evolved from animals—in short, to be animals themselves.
Nevertheless, we do make commonsense distinctions between what is usually animal and what is usually human. Thus, we are back to what might be called a problem of origins: Did the word "purr" begin life as descriptor for the sound a cat makes and then migrate over to describe certain human noises and, from there, get assigned to inanimate objects? Or did it start as a descriptor of human noises and migrate to cats? Depending on which is true, purring would become either personification or zoomorphism, and the same would be true of any other word. If we want to get technical, the best way to determine the literary category in which to place a word would be to find a good dictionary that traces word etymology and follow its wisdom.
Otherwise, common sense is a good guide. For example, to my mind, a purr is more associated with a cat than a human, so I would call a purring sidewalk an example of zoomorphism. In other cases, absent a word root, I would advise you to make an educated and context-based determination.