Is the Grand Nagus equivalent to a king? A dictator? Certainly he's not so cruel, but does he have total rule over the Ferengi government and Ferengi citizens?
He controls allocation of trade territories and other business matters
According to the official Star Trek Encyclopedia, written and maintained by the Okudas (Michael and Denise, long-time Star Trek production designers):
Nagus, Grand. Ferengi Master of Commerce. The Grand Nagus has enormous power over Ferengi business, controlling the allocation of trade territories and other commercial opportunities.
Essentially, he is the personification of the business interests of the Ferengi Alliance, overseeing the expansion and negotiation of its trade territories and the investment in, and control of, commercial ventures.
This is consistent with his portrayal in DS9; for instance, when he sends Quark on an exploratory mission of the Gamma Quadrant related to trade of tulaberry wine ("Rules of Acquisition").
In a sense he is the chief financial officer of the Ferengi Alliance and such is not above the law or criticism — for instance, he narrowly defeated a Ferengi Commerce Authority inquest led by liquidator Brunt, and in "Profit and Lace" it was mentioned that the FCA has the power to appoint or reject a Grand Nagus.