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

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

“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.