The thermally activated desorption of dissociated diatomic species from a metallic surface is described as a lattice-gas problem on a square lattice with nearest- and next-nearest neighbor interactions between the adsorbates and investigated within dynamic Monte Carlo simulations. In the limit of fast diffusion with respect to desorption, it can be shown that the desorption rate depends directly on the local order induced by the interactions within the adsorbate layer. Therefore, by employing an appropriate quasi-equilibrium cluster approximation for the local order (beyond the quasi-chemical approximation), a differential equation can be derived that depends on self-consistently calculated structure forms, reproducing quantitatively the temperature-programmed desorption spectra simulated with the Monte Carlo procedure. In this way it can be shown that the time evolution obtained from the dynamic Monte Carlo algorithm is indeed "correct," and on the other hand, that it can be successfully substituted by a "cheaper" cluster approximation.