Yes, that's roughly what I thought before reading it too. The part that's a bit more surprising is that credit cards also make money via marketing, through their rewards programs. Getting you to buy from one merchant versus another one by giving discounts is apparently very lucrative? You can put that under "charging the merchants" but this is something the larger merchants do deliberately to drum up business, like buying advertising.

Airline and hotel marketing, in particular, are big money. From the linked article:

The Financial Times pegs the value of Delta’s loyalty program at a whopping $26 billion, American Airlines at $24 billion, and United at $20 billion. All of these valuations are comfortably above the market capitalization of the airlines themselves — Delta is worth $19 billion, American $6 billion, and United $10 billion. In other words, if you take away the loyalty program, Delta’s real-world airline operation — with hundreds of planes, a world-beating maintenance operation, landing rights, brand recognition, and experienced executives — is worth roughly negative $7 billion. But economics of the loyalty program don’t work without a robust airline operation.

That's an article from a year ago, and it looks like airline stocks have recovered somewhat.

It seems similar to how Google mostly makes money from selling ads. It's a bigger business than I expected back when I started there.

I mostly ignore rewards programs, but I've met people who are totally into them.