The following reading is only partly against the grain, I think...
The state is the unacknowledged center of Laclau's theory of hegemony. In On Populist Reason, he declares that "social demands" are the "smallest unit" of political analysis (73). But these demands are addressed to an institution or authority, an "institutional system" (73), "the dominant system" (89), or an "institutional order" (116), that is presupposed in and through their articulation. These "democratic demands" are "formulated to the system by an underdog of sorts" (125; emphasis in original). Laclau's examples of such institutional systems include small-scale state structures such as the "local authorities" from which people might seek a resolution to housing problems (73) or, elsewhere, the "city hall" that could improve transport networks ("Populism" 36); his historical case studies, however, all involve nation states. If "a demand is always addressed to someone" (On Populist Reason 86), that "someone" is always, for Laclau, an institution already in a position to satisfy such demands. Indeed, the demand itself recognizes the pre-constituted power of the system that is addressed: "the very fact that a request takes place shows that the decisory power of the higher instance is not put into question" ("Populism" 36). The power of the state as "higher instance" is never questioned either by Laclau, who insists that social demands can be satisfied, and satisfied fully.
When a demand is satisfied, it disappears: it "ceases to be a demand" (On Populist Reason 127). When it is not, it gains "discursive presence" (128). Unsatisfied demands give rise to the people and power bloc as partners in an antagonistic relation: if demands addressed to the state remain unfulfilled, they accumulate and an equivalential relationship is established between them; "they start, at a very incipient level, to constitute the 'people' as a potential historical actor" (74). Thus emerges "an internal antagonistic frontier separating the 'people' from power" (74). But this antagonism also displaces the object of its address. When "an extensive series of social demands" remain unfulfilled, these "popular demands are less and less sustained by a pre-existing differential framework: they have, to a large extent, to construct a new one." Hence, "the identity of the enemy also depends increasingly on a process of political construction" (86). That enemy may be given any of a number of names, such as "the 'regime,' the 'oligarchy,' the 'dominant groups,' and so on" (87). And as Laclau points out, names retrospectively constitute their referents: "the name becomes the ground of the thing" (105). But what is important is the displacement, by which a discursive antagonism replaces an institutional relation. An enemy constituted through populist discourse stands in for the state itself.
At the same time, the populist leader, or rather the tendentially empty signifier that is populist articulation's nodal point, comes to incarnate the sovereign. First the leader is identified with the group: "the equivalential logic leads to singularity, and singularity to identification of the unity of the group with the name of the leader" (On Populist Reason 100). The more successful this process, the more that the populist leader can claim to represent the social whole, the "populus." Of course, in that a populist movement emerges in opposition to the state, this constitution of a "signifying totality" has to be distinguished from "actual ruling" (100): the latter would require institutional power, the power to satisfy or deny social demands. But in so far as a hegemonic project can legitimately claim to represent a "people," its leader can then argue that he embodies the popular sovereignty denied by the illegitimate rule of the "enemy." Indeed, for Laclau, it is by means of its characteristic production of an empty signifier that the logic of populism constructs sovereignty itself, as the "void [that] points to the absent fullness of the community" (170). The principle of populism's transcendent "empty universality" is also the principle that grounds sovereign power. And on this basis, the populist leader demands that his sovereignty is recognized, that he should assume the mantle of the state.
These, then, are populism's characteristic moves. First, it displaces the state through the construction of a discursive antagonist. In the process, institutional power, the power to grant or deny demands, is replaced by an image of power, projected onto an illegitimate enemy. In other words, the stakes of the political game become representational legitimacy, rather than the satisfaction of demands. Second, then, the populist leader assumes representational transcendence, and demands the right to be named sovereign. All this is accomplished by means of a sleight of hand that substitutes hegemony for other forms of politics, and sovereignty for any other conceptions of power. Hence populism can gain institutional power while still maintaining an anti-institutional critique directed at the displaced objects of its antagonistic discourse. But rather than offering a critique of this process, Laclau mirrors it, accepting as we have seen that hegemony is indeed politics tout court. This is true even in Politics and Ideology, ostensibly a work for which Marxism and anti-statism remain fundamental.