Google is most definitely a web crawler. They operate a web crawler with the name of Googlebot which searches for new websites, crawls them, and saves them in the massive search engine database. This is how Google powers its search engine and keeps it fresh with results from new websites. You can learn more about Googlebot over at Google's documentation website.
So yes, Google is a web crawler, but it is not WebCrawler, as WebCrawler is a company, also crawling the web, but not Google.