That's absolutely true. In fact, in economic literature they talk about many-sided markets. It doesn't have to be two. Two is just a simplification. Clearly, you would have in this situation multiple sides. As a simplification, the way I think of this game is between buyers and sellers. I would put together the banks, Visa, and MasterCard on the same side, as part of the platform. That's the key part. They are the middle people who try to bring together lots of buyers, who are consumers, and lots of sellers, who are retailers.
The way I envisage the issue before you is to think about retailers, who are the sellers, and consumers, who are the buyers, and the platform. For me, that's the key word when I'm trying to think about this issue. How does the platform work? Whether or not there are multiple parties within the platform, I think that's quite obvious in this case. It's quite possible to have multiple-sided markets.