They're not chief executives, not nominally, not actually. They're chairman of the board. The only power they have is firing the executives and approving the next one.
Those powers were stripped along with virtually all others from the Swedish monarchy in the 1974's reform of government, and now sits with the speaker. Our royal family isn't a lot more than a well payed magnets for tabloid journalists, so that our real civil-servants can get work done.