I'm being deliberately pedantic, but depending on what kind of representation we use for the neural network (due to rounding) as well as the choice of inference (that is, given a distribution for next token, which one to choose), it
can absolutely be reproducible and completely deterministic.
Though chaotic, which I believe is the better word here - a single letter change may result in widely different results.
We just choose to use more random inference rules, because they have better results.