I think you're trying to limit the meaning of both 'next' and 'prediction' in ways that don't reflect usage and that--if adopted--would severely limit our ability to discuss and evolve what LLMs are actually doing.
There's nothing inherent in either word that forces such a limit; predicting based on what will lead to success as measured by [reward function] is still a prediction.
It's not a prediction of the next move though, and that is the point. It's a prediction of what will happen if you make that move.
So, it's not a next move predictor. It's a game result predictor.