My card does not have an RFID chip... so that definitely wasn't it in my case. They
acquired my numbers somehow and cloned it onto another card (my bank said they were "swipes" and
I had my card in my possession).
When I had my AmEx number stolen a few years back, I called one of the places that the card was fraudulantly used at to obtain the receipt. It showed it as one of those AmEx Gift Cards (that you would buy in the checkout line at Walmart, CVS, Walgreens, etc). That way, it doesn't have a name on it and they can't be asked for ID. I assume that's what they did here as well.
Funny story about my AmEx being stolen... One of the places they used the card was at an Applebee's to buy a couple $100 gift cards. I called and spoke with the manager and he cancelled out the gift cards... so when the scum took their whole family out to eat on MY dime, their gift cards were declined.