Let me put it in another way: there's no "credit card payment system" for payments over the internet. There's Visa, MasterCard, whatever other "card" system. Those don't just facilitate payments for credit cards, but also for other kinds of "cards", which, in my experience, are no less common. Talking about paying by card over the internet doesn't make sense without considering that hordes of people don't use credit cards for that.
Let me put it in another way: there's no "credit card payment system" for payments over the internet. There's Visa, MasterCard, whatever other "card" system. Those don't just facilitate payments for credit cards, but also for other kinds of "cards", which, in my experience, are no less common. Talking about paying by card over the internet doesn't make sense without considering that hordes of people don't use credit cards for that.