Yes, technically you can frame an LLM as a Markov chain by defining the "state" as the entire sequence of previous tokens. But this is a vacuous observation under that definition, literally any deterministic or stochastic process becomes a Markov chain if you make the state space flexible enough. A chess game is a "Markov chain" if the state includes the full board position and move history. The weather is a "Markov chain" if the state includes all relevant atmospheric variables.

The problem is that this definition strips away what makes Markov models useful and interesting as a modeling framework. A “Markov text model” is a low-order Markov model (e.g., n-grams) with a fixed, tractable state and transitions based only on the last k tokens. LLMs aren’t that: they model using un-fixed long-range context (up to the window). For Markov chains, k is non-negotiable. It's a constant, not a variable. Once you make it a variable, near any process can be described as markovian, and the word is useless.

A GPT model would be modelled as an n-gram Markov model where n is the size of the context window. This is slightly useful for getting some crude bounds on the behaviour of GPT models in general, but is not a very efficient way to store a GPT model.