If you think there is a mistake in this argument then I'd like to know where it is: https://markov.dk.workers.dev/.
The whole analogy is just pointless. You might as well call an elephant an Escalade because they weigh the same.
¹ Depending on context window implementation details, but that is the maximum, because the states n tokens back were computed from the n tokens before that. The minimum of course is an order n-1 Markov chain.
I would like to comment that there are a lot of papers out there on what transformers can or can't do that are misleading, often misunderstood, or abstract so far from transformers as implemented and used that they are pure theory.