The current interpretation of quantum mechanics is completely at odds with the statement from the story: "'[the simulation] is still as accurate a simulation of the real universe as there can possibly be. Civilisation - indeed, all of history - should rise on this Earth precisely how it did in reality. There are no chances. It's all worked out to infinitely many decimal places.'"
That's just not quantum mechanics. The "infinitely many decimal places" is a classic mistake (pardon the pun) and indicates a strong deterministic bent to the authors way of thinking about the world.
Clearly, quantum indeterminacy and its implications for a non-deterministic universe are still hard to both understand and get right in fiction.