They indeed are the real thing, made by Herman Miller in Michigan, since AA had an arrangement with the Eames design firm to create the old amenity kit design. I've had one at home for over 30-years (one of my first aspirational purchases when I could barely afford it) and enjoy sitting in the AA ones where they exist (also found in the JFK Flagship lounge but not LAX or ORD, though the main ORD Admirals Club has a few).
In later years the aspirational indulgence was a Panasonic massage chair, after experiencing them in several lounges around the world. Not only does it do a soothing massage, I can pretend I'm sitting on a first class airline seat when I've been grounded for a while!