This article is talking about the question of consciousness as "experience" itself, not necessarily as the state of having some sort of intelligent subject (the "I").
You're very likely right that the functional characteristics of introspection and self-identification can be solved without anything "immaterial", but that still leaves open the question of how experience itself arises.
Well, I am arguing that no, it is not. And I don't see what makes qualia mysterious and different from raw sensor values.
"An organism has conscious mental states if and only if there is something that it is like to be that organism". I would argue that something that has a memory that can contain representations of its own internal states exhibits conscious mental states.
You're very likely right that the functional characteristics of introspection and self-identification can be solved without anything "immaterial", but that still leaves open the question of how experience itself arises.