As an FAA Safety Team Member (24891, https://www.faasafety.gov/FAASTApp/directory/view.aspx?appID...), I can shed more light on this. The FAA owns the skies and provides waivers and this was probably a waived operation from the FAA so they were probably coordinating this on the ground.
Cities, and states can pass laws about where it's legal to operate drones, but no city or state may pass a law restricting the "navigable airspace". New York City's ordinance states that it's "illegal to operate drones from NYC and Manhattan" but that's as far as they can go. It's up to the FAA to decide if an operation is a threat to the public and whether it can be done safely. For drone swarms, the controllers are pre-programmed and have RTK modules providing additional accuracy down to the cm or millimeter compared to meters from GPS and once the modules are loaded and launched the flight can be executed autonomously (however, most of these light shows don't have any sensors so collision avoidance is really within the swarm itself and careful planning to avoid manned aircraft and buildings).
If you'd like to see one of these shows in action from the air (self plug), I have a video from the Independence Day show that occurred in Miami on my channel here -> https://www.youtube.com/watch?v=jWO3Bo1y3B8