I will try my best, but please keep in mind that I have not read anything about this topic aside from the OP.
I presume there are many different theses called materialism, but when I referred to the foundational claim in science, I meant something like this: All concepts appearing in scientific theories must be essentially material in nature. This is, roughly, the restriction which prohibits scientific theories involving miracles and the like.
The philosophical question is whether this claim is meaningful. You probably have already balked, since I used the term "material" without defining it. As I understand it, the difficulty of clearly defining this term is the very heart of Mouline's argument that the thesis is meaningless.
One may ask whether this is, in fact, a claim at the foundation of science at all. Perhaps it is not, in which case Mouline's point that it is meaningless is irrelevant to philosophy of science, but it does seem to me quite common that people (philosophers, scientists, skeptics, etc.) do claim that science is restricted to material causes, effects, etc. quite commonly and that if Mouline is right, such claims are regrettable since they are meaningless.
Take everything I said above with a grain of salt, since I'm not educated on this subject. I'm taking my best shot at interpreting a second-hand summary of the article. (I think that Mouline was not just talking about the foundation of science thesis, by the way, but materialism in various other contexts as well, but I chose to focus on so-called scientific materialism.)
I hope that helps. Obviously, I'm not one to speak with any authority on this article.