In the article I made 3 claims, and I agree it was a bit clumsy.

1st I say that "working forwards" in the sense of outputting one token at a time could be some form of prediction, I don't argue against that. This is what LLMs do at inference time.

2nd I say that to me what really constitutes a prediction is the pre-training. Here it's the classic setting for the word prediction in ML. The model outputs a prediction of the ground truth label: the next token.

3rd I argue that in RL there is no ground truth next token, so prediction doesn't apply here anymore.

Back to your question then: you're asking points 3 and 1 are different. Working backwards from a set of win states is basically what RL does in training. Working forward from the current state is what inference does. To me there is a distinction worth thinking about. First between the mechanism at inference time and at train time. Then between what happens in pre-training vs. RL post training.