"Credit card companies trading at 20x times revenue" - this is not appropriate metric to take for those companies.

Price/revenue multiple of Visa/Mastercard is irrelevant because they are massively profitable with 55%-70% EBITDA margin, while Airbnb is not. And thus card networks are trading at around 30x times EV/EBITDA and 45x times P/E, for 2020 expected numbers.

So card companies are not appropriate comparable for Airbnb, even though there is a similarity in business model as double sided marketplaces.

Valuation of Airbnb will be sophisticated and massive number crunching work where investment bankers will be running lots of different methods, triangulating results, and then evaluating investors' actual views during the IPO roadshow and market sounding. This will be quite an exercise.