The main product of AMEX is access to its cardholders.
Because they are picky about who receives their card, an amex cardholder is likely to spend more than a cardholder of another network.
This is why businesses accept amex despite the much higher merchant fees; the higher spending by the cardholders means that businesses accepting amex tend to come out ahead anyway, by virtue of selling more to amex cardholders.
It is a charge card which sets them apart from the credit card business and brings a higher yield to AMEX, the business.