The original premise 3 doesn't include an explanation of why S does A. Your reformulation of 3 doesn't just explicate the meaning of determinism, it changes the premise entirely. Huemer doesn't provide a definition of determinism in the text. But whatever determinism is, by his stipulation, if it's true, then at any given time you only ever have one thing that you can do (if S can do A, S does A).

You can define determinism through physical laws and prior states of the universe if you like, but that doesn't really impact the argument. How does the ability of beliefs to influence past states of the universe come into this at all? Huemer reasons that the premises entail that if determinism is true, then free will is true. This isn't meaningless, it's just taken to be a contradiction. Through reductio ad absurdum, he concludes that determism must therefore be false.