Hmm.
All livestock is domesticated. Even ostrich and buffalo that have been raised by humans know who feeds them and how to make nice.
If a chicken is supposedly "livestock", that is to say, something related closely to an animal used for food, wool, milk, or leather, then dogs are livestock too, are they not?
The Aztecs used to have Chihuahua-like hairless dogs they raised for food, and in parts of Asia dogs and cats are still eaten. The word "budgerigar" is from an Australian Aboriginal phrase for "good to eat", and parrots are regularly hunted for food by some indigenous South American tribes.
However, the evidence suggests that in China domesticated fowl were *not* used for food originally, and were kept as pets or for religious purposes.
Where would horses fit in to all this: they were never raised for food, leather, milk or meat. They were for transportation, until the automobile made them obsolete. So now the only reason to keep horses is for entertainment. They are therefore not livestock and you can have one in your living room.