I don't think "monopoly" is best judged by "current market share", but by whether a) it's easy for users to switch, and b) whether having that market share is self-reinforcing in a way that prevents competitors from entering.
The parent's point was that a) is not true for Google as a search engine.
b) doesn't seem to be true either; while money and experience can make you provide better search results, you don't get an advantage just from a high current percentage of searches.
In a trivial sense you can "SilasX has a monopoly on SilasX's labor" or "Joe Schmoe has a monopoly on hot dogs sold at Elm & Main St". That's not the monopoly anyone cares about. What matters is whether it's difficult to bring online the alternatives to employing my labor or buying a hot dog in that vicinity. In that respect, Google's monopoly on search is not the worrisome kind of thing we associate with monopolies.
b) whether having that market share is self-reinforcing in a way that prevents competitors from entering.
The argument is that large market share cause user capture. It is relative trivial to bring online an alterative youtube, but video creators can't switch unless the audience also switch and the audience can't switch unless the creators also switch. A subpar job by youtube won't automatically mean that competitor can disrupt, and a lot of users, content creator, advertisers, basically every type of users has been cited as disliking youtube but being locked in with no realistic alternative.
a) it's easy for users to switch
For google search, online stores that use google for advertisement and getting new customers can't easily switch as that would result in abandon 90% of new customer. They can't just buy their hot dog elsewhere. Online stores have to deal with google, unless their customer base is located elsewhere.
I'm trying to outline a useful definition of "[bad-]monopoly" that captures the stuff we generally care about when we worry about them.
It's important to have a definition that excludes "they're just unusually good and so people happen to be currently buying from them, purely as an issue of merit". (If Joe happens to be the best hot dog vendor on some intersection, that's different than if he can prevent others who want to from opening shop nearby.)
I said Google doesn't count as the kind of bad-monopoly because they're easy to switch away from, and the market share isn't self-reinforcing.
It doesn't follow that Google is easy to take market share from. That could be the case of "legitimately good at what they do", and is not how you should define a worrisome monopoly.
A company being so good that others can't gain market share isn't (necessarily) a bad-monopoly. Only if that difficulty came from the factors above, would it count as a bad-monopoly.
(Those factors being the vendor lock-in and the self-reinforcing aspect.)
He's saying that (1) they have a horizontal monopoly, but not a vertical one. And (2) the monopoly is due to Google's quality. Should they do a subpar job, they would be disrupted.
