The Kappa biochemistry and the M{\\O}D organo-chemistry frameworks are amongst\nthe most intensely developed applications of rewriting theoretical methods in\nthe life sciences to date. A typical feature of these types of rewriting\ntheories is the necessity to implement certain structural constraints on the\nobjects to be rewritten (a protein is empirically found to have a certain\nsignature of sites, a carbon atom can form at most four bonds, ...). In this\npaper, we contribute to the theoretical foundations of these types of rewriting\ntheory a number of conceptual and technical developments that permit to\nimplement a universal theory of continuous-time Markov chains (CTMCs) for\nstochastic rewriting systems. Our core mathematical concepts are a novel rule\nalgebra construction for the relevant setting of rewriting rules with\nconditions, both in Double- and in Sesqui-Pushout semantics, augmented by a\nsuitable stochastic mechanics formalism extension that permits to derive\ndynamical evolution equations for pattern-counting statistics.\n