Well, per everything that Conway's said, it does make a difference - if the experimenter is somehow able to choose which axes to measure after all dice rolls have been fixed, and the mapping of dice roll to measurement result is fixed (and does not depend on which axes the experimenter measures), then that creates a contradiction.
To my mind that's normal quantum behaviour - we see the same thing in the double slit experiment or Bell's inequalities (which this is just a variation on). Quantum behaviour cannot be explained by rolling dice ahead of time, because random results in different possible universes/branches must be uncorrelated with each other, even though we tend to assume that only one of those branches "actually happens". And this result is a cool demonstration of that. But there's no contradiction between that and most people's normal notion of "randomness", IMO.
The most frustrating part is that this is a cool, exciting result; while it doesn't really prove anything that we didn't already know from the Bell inequalities, the fact that everything's discrete makes for a much clearer contradiction. It shows that quantum-mechanical randomness is very fundamental and genuine: it's not just reading dice rolls off some list that was decided ahead of time, unless we want to commit to the idea that the whole universe works that way. But talking about "free will" just obscures and confuses everything.
[1] IMO that part doesn't add anything new or relevant to the result; it's just stapling the existing EPR paradox onto this new paradox.
