Well, my interest was piqued, and poked around a bit, and now I'm even more confused. There appear to be more guesses than actual answers about the nature of the design. The ear speakers I have seen had a sort of flattened cone, but apparently there are other versions that are flat, but with convoluted tapered ribs. To me, that suggests the intention of pistonic motion, but then there is a statement that the surrounds are stiff. I don't know if it's simply a matter of the surrounds having stiffened over time, or whether they were designed that way, but there being a surround at all implies (in my mind, at least) that the driver works by moving back and forth rather than having waves travelling through it - I do not believe the flat speakers the ear is compared to have real surrounds - the styrofoam ones I've seen have a sort of channel in the foam that (they hope) terminates the wave, rather than reflecting it, and the other ones have sufficiently flexible panels so that a surround isn't needed.
But this is all hypothesis, and I can't claim any certainty. I'd like the find the High Fidelity or Stereo Review review from the mid or late 60s that I remember reading back in the 70s.