My karate instructor long ago taught me that my legs were my best weapon,,,, run like hell. He stressed that karate was for defense,, & not offense. Yet,, he also said that if physical confrontation was required,, use the least amount of force to stop it as quickly as possible. Stop someone before hurting someone. Hurt someone before being hurt. Maim someone before being maimed. And kill before being killed.
That said,, watching this video,, the hatchet guy may have been verbally threatening folks,, but he only smashed property. Using deadly force,, (shooting him) most likely would have gotten you prosecuted for excessive use of deadly force. You'd spend a lot of money trying to prove that you felt he was threatening the lives of people. Lots of video going on, and all of that would be used by a liberal minded prosecutor to nail you. ESPECIALLY if there was a difference in race. (Thug is black, I'm white.)
And the people standing around watching & not evading is another thing that would be used to prosecute you because the people didn't feel threatened.
That said,, if I'd been there,, and he pulled that hatchet,, I would have tried to physically take him out w/o the use of my firearm if at all possible. A solid kick to his knee would put him on the floor. When he went down, take away the hatchet. Stop the threat. And if you had a firearm, AND showed restraint it would play in your favor in the justice system.
But it's still NY. And the potential for you to get charged with a crime exists.
Here in NC,, depending upon the county it could be as bad as NYC,, or you would be getting "atta boys" for stopping the hatchet guy.