I think we are zeroing in on a definition we can agree on. Yes, the "self" is a manifestation of dynamic processes in the brain. The "self" is created by mind and exists only as long as the brain generates mind and the persistent "illusion" of self.
My reaction to your article title comes from years of studying Tibetan Buddhism. Nearly all teachers of Tibetan Buddhism argue that the self is an illusion because most people don't conceive of the self as a process. Most people instinctively believe the "self" is a real thing, a soul, something that exists intrinsically independent of the brain and mind. It seems so intuitive to believe the "self" is something more than an activity of the mind that most people don't question it. Many people will argue with intense emotion that they are in fact real and substantial, and that intrinsic essence will survive death. That's wishful thinking, in my opinion.
If you polled 100 people and asked them what characteristics the "self" has, nearly all of them would say there is an intrinsically existent essence that does not depend on the brain and mind. After years of discussions with people on this topic, whenever I hear someone argue the "self" exists, I immediately assume they are aguing for what I described above. That doesn't appear to be what you are arguing for.
Let me turn the question around on you. What would it take for you to accept the idea that the self is an illusion? What distinguishes "real" from "illusory?"
If I go to a movie, the characters are an illusion. You could argue that they are real because I am watching them on the screen and the projection exists, but I don't think you would argue that the images on the screen are "real."
In the same way, the self is both real and illusory. The sense of self is very real and impossible to deny; however, that sense of self is illusory, just like the images on a movie screen.