Do you mean your card has your IBAN code on it? It sounds like you have a card that is specifically only meant to do ATM withdrawals/deposits, and it can’t make online transactions. This is not specific to Itch.io, but most (all?) sites out there.
A card meant for online purchases should only have numbers on it, regardless of debit or credit. I would suggest to contact your bank when convenient, and let them know that you want a debit card for online purchases, and they should provide you one free of charge (or maybe with minimal costs).