> Long term it should not decrease the supply of housing. Visitors are either going to stay in airbnbs, with friends, or at hotels.

This is a slices-of-pie argument, neglecting changes in the size of the pie. By being a better value than hotels, airbnbs make traveling more attractive, meaning there will be somewhat more visitors and that they will stay longer. I think this is on balance a good thing for NYC (tourism is an industry, after all) but it does put a little more stress on an already-tight housing market.