"A noted Google-watcher has assembled a convincing argument that the site's search results highly favor Google-owned services, despite repeated company claims that they are algorithmically generated and never manipulated."
"Algorithmic" and "unbiased" are not mutually exclusive. They are not even based on the same measurement. "Algorithmic" simply means an internally consistent (generally automated) process is involved. It says absolutely nothing of the validity or impartiality of that process. So far as I can tell, there is no discussion here, because the two sides are talking about completely different things.
The argument about click-through rates is poorly thought out as well, as that is certainly not the only (possibly not even the first) metric by which potential results should be judged. Furthermore, the click-through rates quoted by the researchers do not reflect the search engines' click-through rates, but those supplied by third parties. Based on the information in the report, the researchers simply assumed that the click-through data was appropriate and relevant to the search engines' algorithms. However, without further evidence, an equally valid conclusion is that the third-party data does not accurately reflect the search engines' internal data -- and given that the third-party data is by definition specific subsets of search engine data, the potential for bias in them is strong.
In short, search engines are black boxes, the companies that run them intentionally keep them that way, and as long as they remain that way, research like this only reflects guesses that may or may not reflect reality. The guesses may seem intelligent and logical, but without the core search engine data, they are inherently unverifiable.