Your example is too sparse to make a conclusion from

I’d offer an alternative interpretation: LLMs follow the Markov Decison modeling properties to encode the problem but use a very efficient policy for solver for the specific token based action space.

That is to say they are both within the concept of a “markovian problem” but have wildly different path solvers. MCMC is a solver for an MDP, as is an attention network

So same same, but different