What does "computational phenomenon" even mean?
I really don't see how any of the ideas presented in the text prove that "it cannot be sufficient", nor it's clear from the text what "physical phenomenon" author has in mind?
Brain is a network of 86 billion organic electro-chemical switches making 100+ trillion inter-connections, each either firing electrical impulses or not... so how it that not "computational" in it's nature? There're also chemical reactions going on that influence neurons and possibly some EM field interferences play roles, too, but that's all part of the "hardware"'s internal design.
Brain is, of course, not really modeled like general purpose programmable computers that we're used to today, more like old concept of specialized hardware machines and automata (or perhaps today's FPGA concept) - it comes with the programming implemented in the hardware itself. The obvious difference is that brain is incomprehensibly more complex than anything we can build, and also being made of living tissue capable of re-arranging and re-purposing tricks that no silicon based computer will ever be able to do - but in the end, it's still a "computational machine" processing inputs and internal states and generating some results based on that... how else to call it without going into the spiritual stuff?