Is veterinary physiotherapy recognised in Aotearoa | New Zealand under the Health Practitioners Competence Assurance Act (HPCA)?

No. Under the HPCA Act the practice of physiotherapy in New Zealand is limited to humans. 

An extract from the prescribed General Scope of Practice: Physiotherapist is shown below (with emphasis added).

“Physiotherapists are registered health practitioners who are educated to practise autonomously by applying scientific knowledge and clinical reasoning to assess, diagnose and manage human function.”