AirBNB units make up 1/5 of 1% of the NYC's rental units. A bottleneck? no, but sizable and impactful, especially when you consider that these tend to be clustered around where they're convenient.
Convenient is not the right description -- high demand is. Who's to say an AirBnB is a worse use of space for, say, a unit in SoHo than a year-round resident?
AirBnB has real issues -- zoning, hotel tax, safety, etc -- but politicians like to use rent cost/resident displacement because it's an easy rallying call.