I fully agree billionaries have far more influence than I do. So do many elected officials, including Mitch McConnell. That isn't the issue, at all.
Bill Gates is out there spending his money to "make the world better" as he sees it, maybe he is sincere. Koch is out there spending money to do the same by influencing the political process, the two have opposing views on most things. Arthur Blank spends his monies on sports teams, and hospitals with his name on it. That's a fair bit of influence around here.
Then you have autocrats of major countries like Russia and China with a lot of influence, their aims are pretty much opposed to leaders in the Western world, who have influence. The Pope has influence over most Catholics, it's of a different kind of course.
You have a lot of folks with influence, but their aims often compete and contrast. No smallish group of them "run the world".