Your link explains that the issuing banks charge interest, not the credit card companies - which are merely the payment processors. I don't know all of the companies listed, it's possible that some are two in one and have their own bank as well. Some payment processors are partly owned by major banks too. But take the largest CC company, Visa: They don't extend credit at all, they don't even issue their own cards iirc. All their profit comes from fees, because the fees are too damn high™.

They've successfully convinced the public of the opposite though. It's a very common misconception that only "suckers" who buy on credit pay for it and that everyone else is getting a free service as long as they pay off their cards in time. In reality everyone pays because the merchants have to pay those fees and they pass the cost on to the consumer.