The American antitrust law (as I understand it, I'm not a lawyer) allows you to create and have a monopoly. What's illegal is using your monopoly in one market to muscle your way into another. The classical case is Microsoft having a monopoly on operating systems, and abusing that to dominate the browser market.
As I see the argument made by the author he is saying that Google has a monopoly on search, and that they are using that monopoly to dominate the advertising market.
"he is saying that Google has a monopoly on search, and that they are using that monopoly to dominate the advertising market"
That's also what I thought he meant. The problem is that search isn't a market. They dominate the search based advertising market because they dominate search (which is not a market in and of itself, it's free content that gets eyeballs like a TV show).
And in my opinion at least they are great at their ad distribution business (where the ads go on other people's sites) because of their high value brand, not from some sinister tactic they are able to inflict because of their dominant search engine.
It is interesting to me when people say that "search is not a market". So pardon my ignorance but if search isn't a market, why (in the case of antitrust clauses against Microsoft) are browsers a market?
The most salient point I saw there was that Google is using its search power to subsidize Gmail, gDrive, Google Office, etc. In my opinion, search is a narrow, competitive enough market that you can't break it up, but you can force Google to separate Gmail from search, and make Gmail pay for itself through its ads.
Will it happen? I'm not sure. But I think he had a pretty strong start to a case that argued Google controls too much of the general online market.
As I see the argument made by the author he is saying that Google has a monopoly on search, and that they are using that monopoly to dominate the advertising market.