The Argument Against Determinism from Newcomb's Paradox

To the esteemed Rabbi, greetings.
In the book The Science of Freedom, an argument against determinism is presented from Newcomb's paradox, and the late author on page 153 ("Further clarification of Newcomb's paradox"):
"But further observation shows that the determinist's difficulty remains. Our problem is not about what the voter would do in such a situation, but what is right for him to do. This is a mathematical question about strategy, which belongs to game theory, and not a question about the psychology of the voter or what will actually happen. Even in the deterministic picture, which holds that none of us have freedom of choice, the question can be asked: Assuming that some creature in some imaginary world has freedom of choice, what would be more right for him to do? There is no answer to this question, and this is the very problem that arises in the deterministic picture," he said.
And I didn't understand. After all, even the determinist would agree that "assuming that there is some kind of imaginary world, some kind of freedom of choice," then the whole problem doesn't begin because even the prophet doesn't know what doesn't exist (and as explained before, that's what the libertarian believes). So where is there an argument against the determinist here? He's basically saying that our Earth is different from this imaginary world.