The discussion of whether or not we have free will strikes me as confused. Aaronson suggests that we would clearly not have free will in a scenario where “Everything [we] did could be fully traced to causal antecedents external to [us], plus pure randomness—not in some philosophical imagination, but for real, and on a routine basis”. The caveat “external to [us]” is doing a lot of work here, but it really has no discernible meaning. (Is a cause “external to us” if it’s not within our brains? Why would that matter? What is the status of chains of causation that lead from the outside world to goings on in our brains?) Without that essentially meaningless caveat, the statement is simply a trivially true disjunction of the logical possibilities given physicalism.
Of course, if physicalism is true, then everything that we do is either determined by the laws of physics or not determined by anything. If that entails that we don’t have free will, then Aaronson should just say that he thinks physicalism is true and that he thinks that physicalism entails the absence of free will. On the other hand, if we don’t simply assume physicalism, then the fact that our behavior is determined by the laws of physics really does nothing to argue against free will. Everything would hang on how minds interact with physical reality, and we simply know nothing about how that might work. For example, it might be that God ensures that the physical world operates so as to respect the free decisions made by our minds. Or it might be that phenomena which are random from the point of view of physics are (sometimes) linked to free decisions made by minds. Nothing is known, so nothing can be concluded.
I'd also have to say that Aaronson lacks imagination in a crucial respect. He claims that in any "imaginable" universe it will hold that "if you knew the complete state of the universe, you could use it to calculate [either deterministically or probabilistically] everything I’d do in the future." But of course it's very easy to imagine a universe where this is not the case. E.g., any universe where minds make free decisions that lack physical causes. We know that people have in fact imagined this sort of universe.