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.