One of the best things about Airbnb is it has made travel more accessible to the young and the working-class. When those people visit NYC, they shop, they eat out, they see shows. All of those things are taxed.
I would bet that the sale tax for all of those things would more than make up for a loss in hotel tax revenue, if you presume that some percent of visitors would not visit if they had to pay for a traditional hotel.
Unfortunately few legislatures and regulators think this way. They spend too much time thinking about how to take a larger portion of the pie and not much time thinking about how to make the pie bigger.
NYC government also seems to think they'll be able to put the genie back in the bottle -- I think they're wrong. Airbnb has proven this is a huge market -- if they go under, they'll be replaced by a solution that is harder to regulate.