Well I guess maybe it's true that you can turn any stochastic process into a Markov Chain by changing the state space somehow (for example the states could be sample trajectories up to some finite time T). And while this is true it may be not very insightful.

But I personally think that to understand LLMs it is much better to think of the whole context window as a state rather than the individual states. If you modelled a simple register-instruction computer as a stochatic process, would you take the states to be (address last symbol written, last symbol written)? It makes much more sense to take the whole memory as a state. Similarly a transformer operates on its memory, the context window, so that should be seen as the state. This makes it clear that seeing it as just a stochastic parrot is misleading, as its all about conditioning the distribution of the next token via prompt engineering the previous tokens. And it is nevertheless a Markov chain with this state space.