I was confused by the way he was using the term "non-determinism". Then I read this:

It's important to understand that computer scientists use the term "nondeterministic" differently from how it's typically used in other sciences. A nondeterministic TM is actually deterministic in the physics sense

-Theoretical Computer Science Stack Exchange

Assuming that person was correct, then it seems like Aaronson is responding to an argument that uses the physics sense of "non-determined", but replying with the CS sense--which I'm thinking makes a difference in this case. But that's just what it seems like to me--I must be misunderstanding something (probably a lot of things).