I've read Marx, quite a lot, actually.
This executive power with its enormous bureaucratic and military organization, with its vast and ingenious state machinery, with a host of officials numbering half a million, besides an army of another half a million, this appalling parasitic body, which enmeshes the body of French society and chokes all its pores, sprang up in the days of the absolute monarchy, with the decay of the feudal system, which it helped to hasten.
He was talking about the French state. You're actually taking a metaphysical approach to Marx, not a dialectical one, by trying to abstract points away from the necessary context they exist in.
Classes are social relations to production and distribution. When production is collectivized and owned by all, it still needs managers, what Engels refers to as the "administration of things." Further still, between capitalism and communism there is the transition from one to the other, that is still heavily made up of elements of the old as elements of the new grow and overtake it.
This is basic dialectics.