"A monopoly (from Greek monos μόνος (alone or single) + polein πωλεῖν (to sell)) exists when a specific person or enterprise is the only supplier of a particular commodity.
Monopolies are thus characterized by a lack of economic competition to produce the good or service and a lack of viable substitute goods. The verb "monopolize" refers to the process by which a company gains the ability to raise prices or exclude competitors." - Wikipedia
You can monopolize an market by popularity, and thus create a monopoly. However, monopoly and popularity is not the same word.
You are interpreting "monopoly" literally. In the context of antitrust law, you only need to have a big enough market share to appear on regulators' radars. The actual market share threshold varies from country to country, but typically it's around 60%. Google certainly meets that criteria in many countries, not only for search but for online video as well.
As for "excluding competitors", Google is having a tough time with antitrust regulators in the EU for exactly that. For a more obvious example, see their shenanigans with YouTube and Windows Phone.
I totally don't buy that Google has a monopoly on search. Anyone here could start a search engine tomorrow. Sure, it might suck, but there is no barrier to entry. It isn't like Ma Bell telephone companies who had blocked other competitors from running copper wires to homes via tons of local ordinances... which reminds me, its pretty hard to have a true monopoly without some help from the government.
You can monopolize an market by popularity, and thus create a monopoly. However, monopoly and popularity is not the same word.