This is the Ego Depletion hypothesis. When the article was written in 2013 it seemed very likely to be true. In 2016 we're now aware of serious problems in many psychology studies, and while it's not definitely proven false, it's failed to replicate in enough studies that there's major doubt about it being a real effect.
https://en.wikipedia.org/wiki/Ego_depletion#Reproducibility_... https://en.wikipedia.org/wiki/Replication_crisis