Similarly, I felt I had a pretty watertight claim as they could see a second ride which I would have to have teleported back to the airport to take. And I could cope financially even if the refund hadn't come through - it was more the frustration in the moment that I wasn't able to get anywhere or (seemingly) get any help. A good call on a chargeback though, that never occurred to me but clearly failure to provide a service charged for would be fair grounds.
I think this is the only bad experience I've had with Uber, and to be honest I'm largely annoyed at myself for not having been better prepared / informed. You even get given a free sim card on arrival, I just didn't have the appropriate tool to put it in my phone! Anyway, lessons learnt if I do transit through again some day - but I'm in no rush to do so.