The wikipedia entry considers the issue, presents data that are curious with respect ot the data in the Economist article, saying domestication is presumed from wolves roughly 14,000 years or so ago.
https://en.wikipedia.org/wiki/Dog#Taxonomy
The Economist article hints at the curiosity, in mentioning pre-Colombian dogs in the Americas were distinct some 23,000 years ago, but then returns to the standard presumptions.
An article in Nature also considers the ancestry presumptions