The ubiquity of prompted hallucinations demonstrate that LLMs talk about a lot of things that they plainly doesn't reason about, even though they can demonstrate "logic-like" activities. (It was quite trivial to get GPT3 to generate incorrect answers to logical puzzles a human could trivially solve, especially when using novel tokens as placeholders, which often seem to confuse its short-term memory. ChatGPT shows improved capabilities in that regard, but it's far from infallible.)
What LLMs seem to demonstrate (and the thesis that the author discards in a single paragraph, without supporting evidence to do so) is that non-sentient AIs can go a very long way to mimicking human thought and, potentially, that fusing LLMs with tools designed to guard against hallucinations (hello, Bing Sydney) could create a class of sub-sentient AIs that generate results virtually indistinguishable from human cognition -- actual p-zombies, in other words. It's a fascinating field of study and practice, but this paper falls into the pit-trap of assuming sentience in the appearance of intelligence.