By definition in New York, certain health professions like chiropractic and massage therapy can only be practiced on humans.
You can see the profession definition for massage therapy at https://www.op.nysed.gov/professions/massage-therapy/license-requirements
You can also find the answer here, on the FAQ page:
No. The scope of practice of massage therapy confines the practice to humans. The only persons who may treat animals using massage therapy techniques are veterinarians and veterinary technicians under the supervision of a veterinarian
So with or without a veterinary license, it is not legal to practice massage therapy on animals in New York State.