I feel a little dissatisfied with this argumentation. As the title of this subsection, and most importantly the main subject of the paper would suggest, the authors should show how language develops. This however gives no account of language. With the above given scenario, we might as well have ended up having a rich conceptual structure, some mimicing or gesturing for communication, but no language at all. Language itself consists of more modules.
Conceptual structure is only a part of the whole model.
The authors should indicate how modules other than CS are mapped into brain anatomy or brain evolution. However, they don't say much about it. They even ignore the purely linguistic modules.