What you are describing is the ascendency of a new third class of people in capitalist systems: the managerial class. Where once you had labourer and capitalist you now increasingly have people with real power derived from their positions within large private organisations and not derived from their direct ownership of capital

https://en.wikipedia.org/wiki/Professional%E2%80%93manageria...

It is a bit of an overused catch-all term though, but explains what you are describing.