Are monopolies strictly and solely defined by market share and not power and influence on the market in addition to abuses done through that power and influence? Defining monopolies only by market shares seems to be an outdated view. Things are different now. Even with that definition though, there is definitely a duopoly.
Strictly speaking, no. Monopoly power has been defined by the Supreme Court as the "power to control prices and exclude competition" and it is not based on a specific market share threshold. However, courts tend to start by examining market share in determining how much power a company has in a given market, and (as I posted in a sibling comment) they typically do not find monopoly power when a company has less than 50% of the market.
