Even if you could understand human cognition to the level required to say, confidently, that it’s done one word at a time, it’s likely not!
I think they’re not talking about cognition, but about output: regardless of what may be happening inside your brain, ultimately one word at a time comes out of your mouth, right? And you can’t then unsay it.
When you put it in those terms, LLMs are in exactly the same boat.