Recent experiments on the oxidation of ultrathin Mg films have revealed the existence of a correlation between surface reactivity and quantum-size effects. Using ab initio density-functional calculations, we have investigated the electronic properties of epitaxial Mg(0001) films, 5\char21{}17 atomic-layer thick, on a W(110) substrate to clarify the origin of this correlation. We find that the decay length in vacuum of the thin-film local density of states at the Fermi energy exhibits a pronounced oscillatory behavior as a function of film thickness. This is expected to have a major impact on the electron transfer rate by resonant tunneling, which is believed to control the initial sticking of ${\text{O}}_{2}$ molecules in the oxidation process. We have also examined the atomic-scale properties of the surface, interface, and quantum-well states of the Mg(0001) films on tungsten and the influence of epitaxial strain on the electronic states, in connection with the interpretation of recent photoemission spectra on these systems. In particular, we find strongly coupled surface-interface resonant states that originate from the Shockley surface states of the films. Comparison with photoemission measurements allows an unambiguous identification of the corresponding surface-interface-state splitting.