The network is available on IntegromeDB public database (http://integromedb.org) under the present manuscript title.
So I went there:
Apparently, typing in journal article titles was not what the search field was for. Couldn’t find the network either, but the article is still in provisional pdf form so that may be the reason.
Dragana Stanley, Nathan S Watson-Haigh, Christopher JE Cowled, Robert J Moore. (2013) Genetic architecture of gene expression in the chicken. BMC Genomics 14