They have a duopoly [1]. The linked article explains what a duopoly is, and cites relevant examples. I can tell you of another very relevant US-centric example but its not in business: Republican and democrat.
The impact a duopoly has on a market is vastly different from a monopoly. One problem could be price fixing; but that could happen with more than 2 companies as well. Then we speak of a cartel.
The problem with a monopoly isn't per se that it exists; it becomes anti competitive business practices when the monopoly is abused to exercise control over other markets. I'd like to compare it with a benign tumor which ends up spreading.
[1] https://en.wikipedia.org/wiki/Duopoly