This is NOT something new. I do NOT rule out somebody fighting it up through the courts. Why is it to be "illegal" for them to rent for one week, but okay to rent for a month or for a yearly lease?
Before AirBnB, there was another site which was successful. VRBO, standing for "vacation rentals by owner."
They do more or less the same function, and there are others. They allow individual property owners to rent all or parts of properties, for short terms.
I have some knowledge, as a real estate broker in what is becoming more and more, a resort area (California coast).
I do not deal in the market, per se. There is nothing new about the market. People have owned resort properties, and have rented them all over the world.
A friend of many years had a beach house, in Ocean Beach Maryland for example. He essentially "turned it over" to a local specialty broker, who handled everything.
Neighbors MAY object to having short term people in their vicinity.
Most important is the local taxing jurisdiction which feels "entitled" to reap revenue from economic activities. Hence daily "room taxes, permitting and inspection fees" etc.
To some extent, AirBnB is like Uber, in that they facilitate commerce directly between willing parties. The objection comes from other parties, which are losing business and taxes.
VRBO was in place as an internet website, long before AirBnB, which is a mobile App.
Mobile Apps are fast substituting and growing the market for their uses. In real estate something like 2/3 + of searches are from mobile apps, not big screen websites.