To be clear (and maybe pedantic), I don’t think that list actually says anything about whether Apple Pay is accepted. Apple Pay (unlike PayPal, for example) is just a way of processing a regular credit card (or debit) transaction. So it would still be a Visa or MasterCard or other credit card payment. (Ditto Google Pay, I believe.) Whether AA has enabled support for Apple Pay is a separate question from which credit cards and other payment types they accept.

But I don’t know one way or the other. Usually it’s pretty obvious how to choose Apple Pay if offered, and it’s definitely a minority of online retailers that offer it, so I would assume AA doesn’t if the OP didn’t see it.