Physics models of closed systems moving under classical mechanics are deterministic, continuous Markov processes. Random walks on a graph are non deterministic, discrete Markov processes.
You may further generalize that if a process has state X, and the prior N states contribute to predicting the next state, you can make a new process whose state is an N-vector of Xs, and the graph connecting those states reduces the evolution of the system to a random walk on a graph, and thus a Markov process.
Thus any system where the best possible model of its evolution requires you to examine at most finitely many consecutive states immediately preceding the current state is a Markov process.
For example, an LLM that will process a finite context window of tokens and then emit a weighted random token is most definitely a Markov process.