Crypto payment in a web shop isn't even a real use case. What they do is send crypto to a third party which sells it for fiat and then the good is paid with fiat. Does that need crypto? No that would work with anything else. The Code on a Paypal PSC for example isn't a crypto coin/token but it can do the exact same thing just better in most cases. The reason you can buy stuff with crypto in web shops is because people wanted to not because it makes sense to do that. It would kinda make sense if there would be a world current with rather stable value. But stable coins are IOUs aka debt so they are not really cryptos.
They get fiat whenever someone makes crypto payments to them. The payment can be stooped by anyone in between like the exchange the bank of said exchange or the web shops bank who gets the payment form the exchanges bank. None of these web stores circumvent the payment processor oligopoly.
