If you still think there's something left to explain, I recommend you read your other responses. Being restricted to the training data is not a property of Markov output. You'd have to be very, very badly confused to think that it was. (And it should be noted that a Markov chain itself doesn't contain any training data, as is also true of an LLM.)
More generally, since an LLM is a Markov chain, it doesn't make sense to try to answer the question "what's the difference between an LLM and a Markov chain?" Here, the question is "what's the difference between a tiny LLM and a Markov chain?", and assuming "tiny" refers to window size, and the Markov chain has a similarly tiny window size, they are the same thing.
More generally, since an LLM is a Markov chain, it doesn't make sense to try to answer the question "what's the difference between an LLM and a Markov chain?" Here, the question is "what's the difference between a tiny LLM and a Markov chain?", and assuming "tiny" refers to window size, and the Markov chain has a similarly tiny window size, they are the same thing.