Depending on the data source, Google has 80%+ share of the search engine market in many countries (such as here in the UK). That's a level often considered monopolistic.
No, that's considered having a large market share. Monopolies do not have competitors and have markets that are difficult for other companies to enter. Google has competition, both search (Bing, Baidu, DDG, etc.) and ads (MSN, Facebook, Twitter, etc.).
Put another way, monopoly companies have a large market share, but not all companies with a large market share are monopolies.
Put another way, monopoly companies have a large market share, but not all companies with a large market share are monopolies.