A literal monopoly is not necessary for a court to determine that a firm can exert significant and durable market power over its competitors and customers.
If a firm is able to achieve and maintain a monopoly solely through lawful and reasonable means, such as producing and offering a superior product at a lower price, it is free to reap the benefits of that fairly-attained monopoly.
That constitutes monopoly and anti-competitive business practices.
But this isn't the real issue. The real issue is that the US hasn't vigorously enforced its own antitrust law in over 20 years, because a policy of "monopolies are good" was adopted in the 80s and has only gotten stronger over the years. (The Microsoft antitrust case of the 1990s was an exception.)
I don’t see how this behavior would be particularly different from John Rockefeller buying up all the means of oil production.
As long as they didn't become a monopoly in any specific creative field, it would be fine too.