The Pythagorean Illuminati are anonymous, but from what I can tell from that interesting interview, Joscha Bach doesn’t share their views. Although Bach likes to use technical terms, I think he subscribes to the standard computational theory of mind. He’s not a metaphysical idealist. He says the mind is the operating system running on the brain, since the brain has to model or simplify itself and its interactions with the rest of the world. Our conscious selves are virtual persons rather than physical things, but the physics comes first, for Bach. The Illuminists reject and even demonize that materialism.
Incidentally, in my first article on Medium, “The Meaningful Life is Storied,” I talk about the extent to which the mind is just a narrative, without going into all the computational jargon.