Actually, I opened a second game and there was a "pay by card" option, which worked. So I suppose it's a per-game setting? Scratch all I said above then.
Viewing post in Alternate payment methods
It's not that simple, game authors on itch.io have the option to collect money directly rather than going through the platform, in which case they're free to support alternate payment methods. But that's an option open to few, since compliance with financial regulations is increasingly difficult these days. For example, I pretty much have to let itch.io collect payments for me, and that does indeed limit who can buy. So your request certainly is justified.