The point the author's trying to make is that if we state in a paper something like "the LLM understands, believes, thinks, ..." then we're supposing an intelligence much like our conception of a human intelligence. It's a form of 'begging the question' -- assuming what you're trying to prove.

It is not quite a fair argument, just because we don't have a precise vocabulary around how to talk about the activity of LLMs that doesn't involve making these loose analogies. Except for philosophers and people engaging in this kind of "is it truly intelligent or no" conversation, being imprecise in this way doesn't necessary have any cost, but is just a convenient way to avoid developing a jargon.