However, USA Gymnastics is not a monopoly, and there are other entities that organize gymnastics competitions (and most gymnastics competitions are not USA Gymnastics competitions). USA Gymnastics is simply the organization that is tasked with overseeing the national championship and Olympic qualifiers.

There is absolutely no monopoly in running. There are literally thousands of different races around the world, and nearly as many race organizers. Each of the big major marathons is organized by a different company. Each of the major track events is put on by a different company. There are dozens of running shoe and apparel brands. There are hundreds of running clubs like Nike's Oregon Project, many of which were just as, or even more successful, as NOP (see, e.g. North Arizona Elite).