The author seems to equivocate between two different options for evaluating claims. First he says that flasification doesn't matter and that "usefulness" is what is really important. Then a few sentences later he switches to claiming that "simplicity of initial conditions" is what actually makes the 10k year theory less useful. That seems confused.

Usefulness is not a sound way to ground your epistemology. The creationist can rightly claim that their 10k year theory is useful in explaining fossils because the complexity of initial conditions is "evidence of the greatness of God". Since the creationist wants to believe, the theory is useful.

I don't think the author really believes anything different than Popper. I think Popper would say that the 10k theory is worse because it is much harder to falsify in principle. That is, there are fewer hypothetical experiments that could falsify it. The author seems like he would agree with that explanation.