The way I understand it, and I could be very wrong, is that it's like brute forcing the universe while wearing a blindfold. Because the power of a qubit is exponentially higher than the same number of bits, you can get a lot more information from the same amount of processing power. However, if you measure the qubit, it loses all of that information. Instead, you have to set parameters that say things like: solve for x, and then you wait for the solution to be presented from the qubits. The catch is that you can't see how the qubits are working, because if you do, you observe them and the data is lost. You just have to hope that they solve the problem for you. In reality, it wouldn't be that strange of a process, because you wouldn't ask it theoreticals, you would have it solve complex problems that can be solved in some way. That's why computer gaming gets no benefit, you aren't asking for answer to complex problem, you are telling polygons where to be.
The rest of the instructions are all valid n-controlled Toffolis and Hadamards, but of course mostly Toffolis since it's replicating a classical algorithm. There is no quantum advantage, it's just a classical algorithm written in a format compatible with a quantum computer.
Add small errors to the quantum simulator (quantum computers always have those) and all'll break entirely - apparently (1) no error correction was used and (2) it's just logic gates for Doom rewritten as quantum gates. No wonder the author got bored, I'd be bored too.