In this specific case, it's not assault. THIS SPECIFIC CASE. However, I then went on to clarify that a slap COULD be assault in other instances where an injury is sustained. But I see you didn't address where I put the statute right in front of you where it actually says that slaps, kicks, and punches can be harassment and not assault. Way to go, bro.
NY Penal Law
S 120.00 Assault in the third degree.
A person is guilty of assault in the third degree when:
1. With intent to cause physical injury to another person, he causes such injury to such person or to a third person