To be fair, GitHub is really part of an oligopoly, comprised of themselves, BitBucket, and GitLab, but the winner of a majority of market share in this situation is typically referred to as a monopoly, in the same sense that Google is referred to as a monopoly, despite the existence of Bing, Yahoo!, and other search engines.
For context, according to Compete, GitHub had 24 times as many unique visits as BitBucket last month. GitLab has about half to one third the traffic of BitBucket.