It is predicting based on a model. In many cases we can download the model off hugging face. The model is conditioned by all sorts of things. Training data, post-training, coincidence, prompt inputs, runtime data available from whatever means.
> but at least I would still call it a "next token predictor"
We can call any prediction system a next token predictor. If you watch over the shoulder of a human writing a HN comment you are almost certain to see them generating a linear string of tokens. That is what keyboards do. It is impossible to generate text without being equivalent to a next token predictor.