Isn’t Times Square a public place?
The Street Activity Permit Office.
https://www1.nyc.gov/site/cecm/permitting/permit-types/press-rallies-demonstrations.page
Not unlike many municipalities who require things like parade permits if your event is going to block a substantial part of a public thoroughfare.
The Times Square Alliance, a “business improvement district” that has state imprimatur, including a dedicated property tax assessment, is the organizer. TSA hires an event planner, Countdown Entertainment, which works with the city’s office of special events (not sure exactly what that’s called in New York) and other departments including the Dept. of Transportation and NYPD on issues like access and security.
It’s pretty common for cities to temporarily close parks, sidewalks, or streets to the general public in order to hold a special event for which there may be security screening, or even an admission charge.
As a public place, it’s owned by the government. And the government can decide how it’s used. You can’t have a picnic in the middle of Seventh Avenue just because it’s a public space. The government has decided that that particular public space is to be used for people to drive their cars on. And the government can decide to temporarily change that space’s use and make it a parade ground or a public meeting place.