So, did some research about the background of the paper. One of the authors:
His website, which features mental health screening tests, was blocked for serving malware that could infect visitors to the site. Epstein emailed "Larry Page, Google's chief executive; David Drummond, Google’s legal counsel; Dr. Epstein's congressman; and journalists from The New York Times, The Washington Post, Wired, and Newsweek."In it, Epstein threatened legal action if the warning concerning his website was not removed, and denied that any problems with his website existed. Several weeks later, Epstein admitted his website had been hacked, but still blamed Google for tarnishing his name and not helping him find the infection.
https://en.wikipedia.org/wiki/Robert_Epstein
And I'd been wondering why the paper was so visibly anti-Google.
edit: I've also been trying to find information about PNAS' peer review process, and this is the first thing I could find that wasn't written by PNAS itself (the link contains both article and comments to the article, encompassing a variety of opinions):
http://www.nature.com/news/scientific-publishing-the-inside-track-1.15424
There's also this background info on politico.com:
https://en.wikipedia.org/wiki/Politico
So, someone had a public beef with Google that turned out to be partly his own fault and all sorts of press got involved, this author is a contributor to Huffington Post, several years later writes a paper about how election results can be swayed by Google, which is suspiciously anti-Google, his paper is hosted on a website whose peer review process is very difficult to find details about, and then a link to the article is posted on a pro-Republican website, at about the same time a liberal potential presidential candidate, Bernie Sanders, is getting a huge, growing amount of attention on the internet, which is heavily associated with Google (it being the most popular search engine), and some are hopeful this internet movement may sway actual votes.
Some of this seems a bit fishy to me.