Eley-Rideal (ER) reactions involving neutral atoms heavier than hydrogen reacting with adsorbed atoms of similar mass were first observed in recent molecular beam experiments by Zaharia et al. [Phys. Rev. Lett. 113, 053201 (2014)]. Through analysis of two types of measurements, they obtained different estimations for the N-O ER reaction cross section, one of which is unexpectedly high. This was qualitatively accounted for by invoking a secondary effect whereby the presence of N adatoms on the surface acted to "shield" O adatoms from prompt recombinative desorption. We apply a rate equation model that includes two ER processes involving different adsorbed species (N-Oad and N-Nad) and an N-adsorption process to the full-beam exposure subset of the experimental data in order to study the reaction kinetics. Values for the individual reaction cross sections are derived. The measured N2 response can be well described by the model, but it is insufficient to completely describe the NO response. Modeling of different exposures is used to evaluate the qualitative picture presented by Zaharia et al.