His theorem doesn't assert free will. It asserts that if experimenters have free will, then particles have free will. So if it's wrong, then it's not for the reason you give.
This isn't a proof of particles having free will. That's an intermediary step to saying we have it as well, and therefore you can start with a step that says we do.
And, whether or not you call this property "free will" is irrelevant to the proof itself; see the final paragraph.
1. Experimenters have free will 2. They're made up of particles 3. Those particles therefore have free will 4. Therefore we have free will (that's why it's called a proof of free will)
Item #1 above assumes the conclusion.
Either the observer's choice of measurements of the particle is completely determined by prior events, and the observer has no free will, or the observer can at his or her whim pick a way to measure the particle. If the latter, then the particle must be able to, also at whim, pick which spin to be measured at.
He never assumes that the observer is made of particles.
The first diagram of the proof starts with "there exists some experimenter with at least some free will". That's a problem, as it uses the argument's conclusion as one of its premises.
Using a simpler example, it'd be like saying, "To prove that aliens exist, let me show you three simple steps: 1) let's assume aliens exist, 2) ...
The second problem here is that he seems to be trying to illustrate that if things cannot be predicted that we have free will. This is a common fallacy in the free will debate. Randomness is an attack on fatalism, but offers ZERO degree of control to humans, and therefore has no place in the free will debate.
Finally, if you want to see a much better argument, in the other direction, check out my Two Lever Argument Against Free Will that uses 25 lines of Ruby.
http://danielmiessler.com/blog/two-lever-free-will-ruby/