The take away is not that the Federalist or Zero Hedge are supposedly unbiased news sources (which they do not claim, they claim to be opinion sites) it's the sheer power that Google has over the media and how at their will they can effectively bankrupt, ban, and silence anyone they choose to with no trial or recourse. This is a disturbing power for anyone to have unchecked whether it be governments or corporations. In the U.S. this is considered an affront to constitutionally guaranteed civil liberties, I know you're from the UK so socially this may not resonate quite the same way.
Google isn't a public service it's a business. It's ironic that free speech gets shut down by the free market; but business is business.
but business is business
That is part of the issue, electric companies, phone companies, etc.. are businesses however they all are required to abide by certain regulations so as to protect public interest. Often there are anti-trust orders to prevent companies from having an undue influence over the public space (Standard Oil, Microsoft, etc..), if you think about Google they control the access to websites and content (largest search engine), the world's largest advertising platform (over 70% of the market), the largest access to data, several of the largest content platforms, and a myriad of other services. If you control what content gets seen and what content is allowed to generate advertising income with such a hugely disproportionate market share, and massive barriers to entry in all of these areas (patents, legislation, resources) do you even have a free market in these areas?
From that Google Communications tweet, they made The Federalist remove their entire comment section in order to not be demonetized. That is pretty fucked up.