Consider how laws are set. Politicians answer to their constituents. If the people who live in the city do not want certain things (short term Airbnb rentals here), you can expect them exert pressure on their representatives to make those things go away. That's exactly what has happened in NYC.

The question of "Why do you think that they should have less rights that people that live in the city full-time?" doesnt really matter. Because the reality is that they have no power/sway over the politicians who are responsible for governing the city.