Tax is paid on profit, profit happens where Airbnb choose to make it happen. Same old same.
ABNB creates externalities to the countries where it operates (increase rent prices), so it would make sense to tax them because of it.
And if they don't like the tax, they are free to stop operating in that country ;)
They chose not to do it to make their platform more competitive with traditional hotels etc, they were able to pocket a significant proportion of it through fees etc. but most of the money went to landlords and clients.
And Italy has rent on gross revenue of rental properties. Which the payment processing party that is Airbnb should collect and pay.
In this case, the tax is paid on the revenue that the landlord makes and Airbnb is supposed to withhold it and pay it to the state. Airbnb being profitable or not is irrelevant.
National subsidiary rakes in money, but has to pay main office in Cayman Island even more in licensing fees for the brand. So national subsidiary is running in negative, and doesn't pay any taxes. Parent company received all the money in Tax haven.