Does the 2013 article criticise Darwinism?

No. Not really. In fact the main thrust of the article is a return to a less dogmatic view which is more in keeping with Darwin’s original ideas.

“In some respects, my article returns to a more nuanced, less dogmatic view of evolutionary theory (see also Müller, 2007; Mesoudi et al. 2013), which is much more in keeping with the spirit of Darwin’s own ideas than is the Neo-Darwinist view.”

Müller GB (2007). Evo–devo: extending the evolutionary synthesis. Nat Rev Genet 8, 943–949. http://www.ncbi.nlm.nih.gov/pubmed/17984972

Mesoudi A, Blanchet S, Charmentier A, Danchin E, Fogarty L, Jablonka E, Laland KN, Morgan TJH, Mueller GB, Odling-Smee FJ & Pojol B. (2013). Is non-genetic inheritance just a proximate mechanism? A corroboration of the extended evolutionary synthesis. Biological Theory 7, 189–195. http://link.springer.com/article/10.1007/s13752-013-0091-5

“One of the major developments of Darwin’s concept of a ‘tree of life’ is that the analogy should be more that of a ‘network of life’ (Doolittle, 1999; Woese & Goldenfeld, 2009).”

DoolittleWF (1999). Phylogenetic classification and the universal tree. Science 284, 2124–2128. http://www.ncbi.nlm.nih.gov/pubmed/10381871

Woese CR & Goldenfeld N (2009). How the micobial world saved evolution from the Scylla of molecular biology and the Charybdis of the modern synthesis. Microbiol Mol Biol Rev 73, 14–21. http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2650883/

The network represents the evidence for extensive exchange of DNA that must have occurred in the early stages of evolution, but which also continued through later stages.

The main departure from Darwin’s ideas is that the ‘tree of life’ is a network: