The author is saying that the output token is not deterministic. I don't think they said the distribution was stochastic.
Even so the distribution of the second token output by the model would be stochastic (unless you condition on the first token). So in that sense there may also be a stochastic probability distribution.
Mostly unrelated (I agree with you, and I'm some ancestory comment you're responding to with the same line of thinking), I have built a couple LLMs where the distribution itself is stochastic. That's not key to how they work as a black box, but much like how quicksort has certain performance characteristics I did find it advantageous to introduce randomness into the model itself.
You could still easily model the next token as a conditional probability distribution though if you wanted; the computation of entropy just might be a bit spendier.
Even so the distribution of the second token output by the model would be stochastic (unless you condition on the first token). So in that sense there may also be a stochastic probability distribution.