Beland is correct in stating that the paper does not show a deep understanding of the volunteer community, though clearly some effort was made. (The sentence "At most there are gentle reminders or "stubs" which editors may attach to articles to suggest changes." shows how completely these efforts failed in some respects.)
Nonetheless the analysis (which compares 3918 pairs of articles, contrary to the impression received by Kosovsky) is valuable.
Firstly it is important to stress that one of the conclusions was that bias per word was less than Britannica. Thus if the Britannica articles had been longer, or the Wikipedia articles shorter, there would have been no significant difference.
Secondly the authors concluded that bias on Wikipedia articles decreases over revisions (and hence over time). This,if true, is an important advantage over standard document production.
The methodology uses vocabulary preferences of members of US congress. It assumes that these reflect the bias of the content, however this makes two assumptions, both of which need supporting evidence.
The biggest flaw is the assumption that the vocabulary represents bias in content, rather than disposition. It is quite possible, indeed likely, that Wikipedia's contributors, especially to US articles are more left-leaning than right leaning. (There are certainly notable - and noble - exceptions.) Writing for Wikipedia is a very different matter than either exhorting through the US Congress, or through the columns of the daily press. It does not follow that those with a political (or other) leaning allow that to affect the content they create to the same extent that they continue to use their politically influenced idiolect.
A second confound that could have been easily dealt with is to remove text not in Wikipedia's voice, for example, quotations and cited article titles.
Finally, it might be worth offering my experience that the bias in Wikipedia is not usually introduced by experienced editors, where the community appears to fail is in allowing itself to be unconsciously influenced into challenging right-leaning statements more readily than left-leaning statements. On the whole, though important, this is a peripheral problem.