There are several problems with author's argument.

1. Future outcomes are not entirely determined by just past state + laws of physics. There is a very important component that author seems to be only eluding fleetingly: Randomness. So future = past + laws + randomness. Here laws are implicitly understood to be probabilistic that requires some randomness source.

2. An all important question now is this: What is the source of randomness in universe? I think if we can answer this question, we will likely have understood pretty much everything that is to be understood about the universe. A perfect random generator is theoretically required to store infinite amount of information. If universe is finite in the sense that (space X time) is finite then perfect true randomness is not possible. BTW, concept of true randomness is not some fuzzy thing. It's very well defined mathematically (see Vol II by Knuth). Summary: Let's say a random number generator produced a sequence of 0s and 1s. The perfectness of RNG can be measured by the distribution of every possible permutation of all length of 0s and 1s occurring in that sequence.

3. Let's say universe has some master random number generator that sources randomness in to all its outcomes. Is it possible to add or subtract randomness from this generator? Can processes or particles within universe themselves be source of randomness? If so these particles or processes would meet the definition of free will. In other words, free will is nothing but random number generator itself because no one can predict or influence its behavior.

So in essence, our question becomes can humans be source of randomness?. As humans are made of same fundamental particles, it would imply, if humans have free will then particles must also have free will (i.e. Convey's Free Will Theorem). The difference that humans make over fundamental particles is this: Humans can filter their free will by setting up complex set of computation on the top of it. So imagine normal particles simply generating random behavior while humans acting as some algorithm like hash function that sets up the computation on the top of their "free will" to generate probabilistically desired outcome. Obviously keyword here is desired. Are our desires simply deterministic or influenced by free will? Our desire to survive is obviously programmed by genes. However our desire to climb a mountain because its there or draw a painting is probably much more influenced by free will.

Since the code will never finish executing, it isn't correct to say that free will has been proven to be an illusion. Even if it could, the most that can be proved to be true is that a certain aspect of the universe is fully determined.

It does not follow that simply because certain aspects of the universe are determined (such as a computer program) that human action is wholly determined. That would be like saying that because certain aspects of the universe are conscious and self-aware, the entire universe is conscious and self-aware.