Just because the credit card company claws the money back doesn't mean that a merchant can't come after you in court/debt collection.
It's not common, but for a big enough transaction, there's nothing stopping a business from coming after you.
This is a misconception that many people have - at least in the US market. I owned an MSP for about a decade, and this was often the most common surprise for merchants: charge backs were final and were actually pre-accepted by the merchant as part of their merchant agreement (it's similar in concept to binding arbitration).
If (in the US) you find yourself being collected after a chargeback... have your lawyer get their hands on the merchant agreement. There are some fantastic consumer protections there.
Where you do see merchant success is where credit cards are being used to make installment payment and the customer stops paying with the card.
It doesn’t mean it will go anywhere if we actually end up in court.
1) once a competent human (and not a third-world boiler room which is what "customer service" is in any large tech company nowadays) looks into it, they may very well make a reasonable decision and rule in the guest's favor to begin with
2) even if they were in the right from a legal/contractual point of view, they'd spend more flying someone out to argue the case in court than to just take the loss right away, so there's still no point defending the case.
3) Airbnb and maybe even the host have skeletons in the closet they'd rather not draw any attention to (search for Airbnb horror stories and you'll notice how they happily profit from obvious, brazen scams and effectively engage in fraud or false-advertising including about their insurance service, and a significant chunk of hosts break their local laws with regards to short-term rentals and/or taxes, which is the only way to make their pricing attractive), so it would be suicide for them to willingly draw any more attention to themselves than they need to.
Plus OP has an excellent story to post as a review since as a 'paying' customer clearly has standing in the matter.
AirBnB has gotten so much bad press over their nit-picky extra charges, fees and required cleaning by guests I would not be surprised if they encourage the 'host' to reconsider their position.