Didn't read the article, but at least based on the excerpts, it sounds like many of these are pretty common misunderstandings of evopsych. E.g.

(2) “Neuroscientists have been aware since the 1980s that the human brain has too much architectural complexity for it to be plausible that genes specify its wiring in detail,”

is quite weak, as discussed in Barrett & Kurzban 2006:

In considering the issue of a gene shortage, it is important to distinguish between architectural modularity and developmental modularity. As discussed in the evolutionary developmental biology literature, an aspect of the phenotype is developmentally modular to the degree that natural selection can act on it independent of other aspects of the phenotype (e.g., Griffiths, in press; Riedl, 1978; Schlosser & Wagner, 2004; Wagner & Altenberg, 1996). Architectural modularity refers to the endpoints of development—the degree to which the phenotype is “chunked” into functional components (e.g., Sperber, 2002). A single developmentally modular process can give rise to multiple architectural modules. For example, the process that produces hair follicles is presumably at least somewhat developmentally modular, yet it produces many millions of individual architectural modules in the form of individual hair follicles.

Does this apply to cognition? Module-like representational structures for face recognition are probably constructed for each face one can reliably recognize even though there are obviously no separate genes for recognizing each one. Architecturally modular novel tokens no more undermine developmental modularity than do novel tokens in other domains. The human immune system generates novel responses to parasites all the time (see, e.g., West-Eberhard, 2003, p. 58), yet no one seems to question whether there are sufficient genes to explain this process. Further, as discussed above, “high-level” modular architectures, such as the cognitive structures underlying chess skill, are probably tokens of module-generating developmental processes designed for other functions. The inference that such systems “cannot be based on a Darwinian algorithm” (Sterelny & Griffiths, 1999, p. 330) is unlicensed. Critics of massive modularity must articulate why novel cognitive tokens are more problematic than novel tokens elsewhere in the phenotype.

Further, developmental processes that give rise to distinct phenotypic structures in the brain presumably share many procedures in common as well as many of their necessary genes (i.e., genes that contribute causally to the development of the structure). Many developmental processes exhibit a nested hierarchical structure: They share common beginning points, with bifurcation or decision points during the process as structures become differentiated from one another and are more precisely specified (Gilbert, Opitz, & Raff, 1996; Riedl, 1978; see especially chap. 4 of West-Eberhard, 2003). Large numbers of modules in the brain might begin from a common starting point, and share many of the processes that build them, the more so the earlier one looks in development. This is a common pattern for evolved developmental systems in general (West-Eberhard, 2003). Subsequently, regulatory processes cause structures to diverge in their development, mediated by inputs from the internal or external world. In fact, different environments might cause different structures to develop by design (because of a history of selection for that outcome) even if there is complete overlap in the genes responsible for the development of the two different structures. [...]

Therefore, the answer to the question “Does each module need ‘its own’ set of dedicated genes?” is no: Finding genes responsible for building that module and only that module is unlikely. Consider the genes “for” (in the sense of Dawkins, 1976) arms and legs. The genes that play a causal role in building arms and in building legs (as well as many other structures) overlap heavily. The same logic applies to the construction of mental modules.

As another way of seeing this, if one tried to specify the number of phenotypic details in the human body that reliably recur during development because of a history of natural selection acting on historically contingent developmental systems, one would certainly find that the number is greater than 30,000, the approximate number of genes in the human genome.6 That is, it would require more than 30,000 parameters to specify the human phenotype in blueprint or informational terms. If such a one-to-one mapping were required, there probably wouldn’t be “enough genes” to build a single cell in the human body (for a similar argument, see Marcus, 2004).

Most of the other numbered points in the second list also seem to be based on similar misunderstandings/misrepresentations of the field.