What you cited is not a statue and is not law.
It is a part of the New York Codes, Rules and Regulations. They are not laws that are voted on by legislatures and signed by the governor. They are rules that are promulgated by state departments.
However, they still have the force of law. According to various lawyers I spoke with, you will not end up in prison for violating these regulations, but you can be fined, lose a license and face other civil charges. The regulations have the force of law, as there are provisions in the law which allow the state agencies to promulgate these rules.
Long story short — it is illegal for a private school teacher to hit a student.
The Wolf