Also not a neurologist, but my reading of it was not the brain is "completely structureless" by any means. More that the 'structures' aren't clearly defined and, crucially, that the 'structures' don't act completely independently from the rest of the brain.
"Pretty much everything that your brain creates, from sights and sounds to memories and emotions, _involves your whole brain_."
They briefly mention that our notion of distinct brain structures may be influenced by our hyper-focus on certain areas of the brain, rather than wholistic study of the brain (because it's expensive).
As a kid, I certainly thought each portion of the brain was independent. As in, I believed that my motor functions came from the clearly distinct "motor function structure" of the brain and without that structure, I would have no motor function at all (and with no ability to regain motor function). I think that is the myth they are referring to.