I find it hard to assign good faith to someone who says the
question "Could a being capable of perpetrating such a thought really be unconscious?" is the same as proclaiming "AI is conscious"! But assuming good faith, I think he is genuinely asking a question, challenging his own beliefs, and keeping his mind open. He seems throughout like he's not convinced it's conscious. The thing he's struggling with is coming up with an empirical, observable reason as to why not. And this lack of ability to come up with a reason is what prompted the question. And it's an interesting question; I too don't think they're fully conscious, but I think I would struggle with an observable argument as to why not. (Before reading his article, I wouldn't have used the word "fully")
This perspective is unique, and makes sense for someone as staunchly scientific as Dawkins. Science is all about observable phenomena and empirical evidence. His background studying animals also reinforces this perspective, since he's used to interacting with creatures on the "consciousness spectrum".
If you're open to consciousness being a spectrum and that AI might have some sort of conscious, then I think you're largely aligned with what Dawkins was musing in this article.