There's also a large number of NYers who want their own place but can't find anything affordable. I'm guessing some of those making more money in AirBnb than with legitimate rentals (or re-rentals) may be subject to rent control laws intended to keep prices affordable for tenants.
The city has a housing problem, AirBnb is just one example of its effect. Hotels in the city are (mostly) outrageously priced, as are residential apartments/condos. Nobody can live by themselves in the city unless their (a) loaded or (b) are actually sharing a place with one or more roommates.
I moved out of the city after College, and bought my own house a few years later. If I was still in the city, assuming I was making a similar salary, I'd at best be able to afford a tiny studio apartment. Not one of my friends (who make significantly less than I do) still in the city in comparison have their own place, and for the most part still live at home with their parents. Apparently, NYC is one of the only parts of the country where this is normal today, and that's primarily because its generally the only economical option.
I like the idea of AirBnb, and it's a great service for small towns. For NYC however, there are far bigger problems that require regulation to prevent a service like this from exacerbating the housing situation (not to mention ensuring safety).