I've been looking into this and it seems that's just the policy of Itch.io. They only have payment through either paypal or stripe, it seems stripe is a third party that handles credit card transactions for them. See if that works for you (is that even an option?) and if not, then we will find another way.
Viewing post in can't pay by card
To be clear, I'm fairly certain that the developer (you) need to enable stripe payments and setup your own stripe account. Once that is done, it should just be a choice for us. https://itch.io/updates/accept-credit-card-payments-with-stripe