The political form
Sacred kingship is the political form in which the king's authority is grounded in his relation to a cosmic-religious order rather than in his relation to a citizen body. The king is the working point of contact between the human polity and the gods (or god, or cosmic principle); his authority is inseparable from his ritual role; the conditions of legitimate rule are not negotiable by the polity because they are not issued by the polity. The classical Mediterranean tradition distinguishes this form sharply from the politeia — the constitutional polity of citizens — and defines its own political life partly by contrast with it.
The two principal ancient cases
The most extensively elaborated ancient sacred-kingship forms are Pharaonic Egypt and Achaemenid Persia.
The Egyptian case is the longer one. The pharaoh's authority, across three thousand years and through episodes of intermediate collapse and restoration, was grounded in his role as the guarantor of ma'at — the right ordering of the cosmos and the polity together. The king's body was treated as ritually distinct; his name carried specific theological weight; his death and burial were the working continuity of the polity's relation to the gods. The Old Kingdom pyramid complex at Giza is the architectural form the early-pharaonic state thought the order required: a monument visible at the scale of the landscape, encoding the king's transition into the eternal order.
The Achaemenid case is shorter but better documented in its political theory. The King of Kings — xšāyaθiya xšāyaθiyānām — derived authority from Ahuramazda, the Wise Lord whose favour grounded the king's legitimacy. The Behistun inscription of Darius I states the principle explicitly: the king rules because Ahuramazda has granted the kingdom, and the king is righteous because the order he maintains is arta — truth / right. The Apadana relief at Persepolis carries the visual statement of the working empire under that authority.
Why the classical tradition defined itself against it
The Greek political tradition treats sacred kingship as the form that the polis is not. Herodotus's account of the Persian debate in Book III on the best constitution — the Greek debate placed in Persian mouths — is the working classical statement: Greek political life proceeds by argument among citizens; Persian political life proceeds by command from a single sacred figure. Greek tragedy (Aeschylus's Persians, Sophocles's Oedipus) elaborates the form as the other that defines the Greek civic experiment.
The Roman Republic inherited the Greek frame and made it more explicit. The Roman senatorial class read regnum as the worst political form, libertas as the absence of it, and the Republican constitution as the working alternative. Tacitus's diagnosis of the Augustan settlement is sharpest precisely because Tacitus reads the Principate as a quasi-sacred kingship dressed in Republican vocabulary — the imperial cult, the Genius Augusti, the divinisation of dead emperors as the visible religious infrastructure of an unfree polity.
What the European tradition kept
The European political tradition received sacred kingship in two principal modes. The first is the medieval Christian elaboration of the rex Christianissimus — the king as the anointed instrument of God's authority over the polity, working through the church but distinct from it. The second is the classical-republican opposition vocabulary — the inheritance from Tacitus, Cicero and the Greek republicans that gave the European tradition the language with which to criticise sacred-kingship claims. Both run through the medieval and early-modern periods; the modern republican tradition emerges in large part from the working of the second against the first.
Why the platform reads it
The platform reads sacred kingship because it is the political form the classical Mediterranean tradition spent most of its political theory defining itself against, and which the European tradition has carried with it in both forms ever since. The question of what grounds political authority — a citizen body's agreement, a king's relation to the cosmic order, something else — is the question every constitutional order has to answer in some form. The classical case is one of the clearer ancient ones for seeing what the alternatives look like and what each of them costs.