Who will interpret "Islamic law", or formulate those laws?
A secular judge? Secular politicians?
Historically, the actual rulers of Islamic states and their subordinate governors (the "executive branch", if you will) has been composed of people who were, of course, devout Muslims, but who weren't members of the
Ulama. That is, the people responsible for making decisions of statecraft, military decisions, even sometimes basic judicial decisions (to an extent...this could and did vary) were not theologians, and didn't make any decisions about points of Islamic law. However, the decisions of these rulers did have to be in line with the
fatwa issued by those actual theologians, and the governors and rulers were often advised by councils of
fuqaha and such.
A really rough comparison would be how the medieval European nobility were not members of the clergy, but still had to rule in line with the principles of Christianity as interpreted and handed down by the clergy, and had to obey Papal and even Episcopal rulings, with high-ranking members of the Church often acting in an advisory capacity when the ruler was making a decision. This isn't an
exact comparison, since the church/state separation happened in European Christianity in a way that it really didn't in Islam, but it at least gives you an idea of how non-clerical rulers can rule according to theological dictates, without those clerics being the actual rulers themselves.
Where Khomeinism diverged from the above pattern was in taking the old Shia principle of
veliyat-e-faqih (though it's not
really all that old) which says that only the
fuqaha, or Islamic theologians who are trained in and focus specifically on the legalistic aspects of that theology (ie, what you can and can't do, as opposed to general theological questions like "what's heaven like") can make rulings and changes to those legalistic theological aspects, and expanding it to cover
everything. That is, instead of merely determining who can be married and deciding legal disputes according to
sharia and letting a non-clerical ruler handle things like military campaigns or opening a new trade route with a neighboring territory,
all of those things would now be handled by one person. And that one person would be a trained and capable
Alim, making the sole and definitive decisions regarding
everything for the entire nation.
As another really really rough comparison, think about the US governmental division of powers. The President is not a member of either Congress or the Supreme Court, but while he can act independently to a degree, his freedom of action is constrained by what Congress instructs and what the Supreme Court interprets. In the style of Islamic rule apparently envisioned by the Brotherhood, simply replace the Supreme Court (and possibly Congress...the Brotherhood has waffled over the years on just how much democracy their hoped-for New Caliphate will actually contain) with a body of Islamic clerics and theologians. Now contrast that to a governmental structure like Iran, which replaces all
three with, effectively, the Pope, who can rule on anything from the legality of a law to who the army is going to invade, all on his own accord.
EDIT: I can't believe I overlooked this in all the above, but Saudi Arabia is, in its basic arrangement, similar to what I mean. The monarchs aren't clerics or theologians, and can technically do whatever they want, but the clerics in the judiciary and the advisory in practice constrain the monarch's actions. Saudi Arabia lacks several of the important elements that the Brotherhood hopes to establish in their hypothetical government, however, and the drift of the Salafi impulse is different between the
Ulema of each country, so Egypt under the Brotherhood won't look exactly like Saudi Arabia. But it'll look a lot closer to that than it will to Iran in terms of basic governmental organization.