Dixie Carter is President and the person that talks to people outside of the wrestling bubble, press, executives, etc. Eric Bischoff is the executive producer, who handles the TV production stuff. Hulk Hogan is GM, who does stuff on Impact.
Jeff Jarrett is a shareholder in the company and the founder. Sting is Sting.
In that aspect, they're not different most other corporations, in that they don't have an overlord.