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.
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.