And if Hotels close down due to AirBNBs there's more space for appartments where there once were hotels. If the AirBNBs take less space than the hotel they replace it's a win for appartments. If they cause more tourism it's a loss. What the overall effect is is far from clear, I haven't seen any thorough analysis on that.

It's naive to only look at one factor and ignore the others, yet that's often how far this debate goes.

Are hotels closing?

It seems very unlikely AirBnBs will "take less space" than a hotel. Hotels are quite space-efficient, given they're largely small, single rooms.