Nothing is stopping someone setting up a competing athletic movement. Indeed, you could argue there are many, many competing competitions (various continental or world championships, world series etc). Its just the Olympics is the one that everyone cares about.
"Oh dear, examine what you've just posted, if you compare Google to the IoC, you've Just said that "no one" competes with them, they're are the governing body."
No, I pointed our your analogy was wrong and suggesting a more accurate version, but hey it's fun to defend a flawed analogy from the person who originally created it. Thus... Google are the governing body of their own results. You can chose not to compete in the Olympics, but then you get no gold medals.
Personally, I think a similar analogy using FIA / Formala 1 works much better, but unfortunately F1 does not have a large following in the US.
In Formula 1, a body that is very much accused of having favourites hands out demotions and time penalties in a more-or-less abitrary way. Some competitors feel discriminated against, while other flagrant infractions go unpunished. Every now and again, there is talk of a breakaway competition, but somehow it never quite happens.