Xavier,
Cool Player ! ! !
Reading the clip you attached, I would say your assessment is far more on the nose than I would have come up with. Sounds like a cathode follower, low gain all current drive, to me.
I'm probably wrong but I have always heard the voltage gain in most amps are in the driver stage(s). I have heard that most output stages increase the "current drive" of the amp.
Like I said, I will probably be proved to be wrong.