is a novel legal theory for restraint of trade. If the damage to the market is to non-Amex customers caused by Amex's market power, then it wouldn't fit the typical anti-trust case pattern.
But it makes you wonder: What if the case is a straight tort? Amex causes damage to non-customers through its actions.
Or you say that it really is anti-trust, in that Amex coerces the merchant into a collusion that fixes the price of transactions in the merchant's shop above what the merchant would otherwise charge non-Amex customers.
In short, I think the danger is very real that Amex could lose the case.
Except there's no coercion and no price fixing by either party.
It's a simple contract: if the merchant wants to accept American Express transactions, the merchant must consent to a condition in contract. American Express is not a monopoly, and the merchant is free to accept or decline the contractual condition.
Either you are not a lawyer, did not listen to the cc or both. Merchants are not forced to accept the card, period. If they agree to accept the card, then they have to be bound by the agreement. Once they decide that "American Express cards are welcome," they can not steer the customer away to another card by giving a better price for the product. If they want to do that, they have to rescind the AP contract. Simple, very simple.