To be honest, it's quite easy, wiki moderators use custom search engines to improve links (especially on heavily discussed or heavily viewed article), here: https://en.wikipedia.org/wiki/Wikipedia:Advanced_source_sear...
if one of the engine return AlterNet or CounterPunch articles on political questions, it's probably "heavily used". If not, the author is a probably a liar, the editor certainly don't check articles and the publication is surely as worthless as AlterNet.
> An external links search shows around 2,580 [1] Wikipedia pages linking to CounterPunch, around 2,400 [2] linking to the Daily Kos, and around 1,640 [3] linking to AlterNet.
Considering how many pages there are on Wikipedia, and how many of these results are notes and talk pages, I think one can conclusively determine that these sites are in fact not "widely used" sources.
This isn't to say they're aren't questionable or shouldn't be filtered against of course (nor that they are and should be).
Then you have sources, the vast majority, that are de facto deprecated, hence are not on any list. If as an example, Counterpunch and AlterNet are never cited except following the 'verifiability policy', they are de facto deprecated, and if it's the case, the author never bothered researching his subject or even reading Wikipedia rules. Which would explain why thecritic is also de facto deprecated.
https://en.m.wikipedia.org/wiki/Wikipedia:Deprecated_sources