It's the hosts they're talking about, not the guests, which would need licenses.
I'm fairly sure you have to have a license to serve breakfast as a business. You also have to be inspected by the health department. Same goes for running a hotel. That stuff all costs money, and it's not up to a private business (AirBnB) to determine how to enforce such laws, even though their existence does change the landscape.
It seems my phrasing was unclear. With "to sleep and eat breakfast", my intent was: a customer to sleep somewhere and eat breakfast there (as the end user), not for a business to serve that customer.
I made this point to the article's literal analogy of the car rental agency's need to validate a consumer to drive a car (as the end user). There is no license needed to sleep and breakfast.
Driving a vehicle (your own or renting someone else's) is an activity requiring a license for the agency to validate.
I'm unaware of any place in the world requiring a license to sleep and eat breakfast.