X-ray observations of shocked gas in novae can provide a useful probe of the dynamics of the ejecta. Here we report on X-ray observations of the nova V959 Mon, which was also detected in GeV gamma-rays with the Fermi satellite. We find that the X-ray spectra are consistent with a two-temperature plasma model with non-solar abundances. We interpret the X-rays as due to shock interaction between the slow equatorial torus and the fast polar outflow that were inferred from radio observations of V959 Mon. We further propose that the hotter component, responsible for most of the flux, is from the reverse shock driven into the fast outflow. We find a systematic drop in the column density of the absorber between Days 60 and 140, consistent with the expectations for such a picture. We present intriguing evidence for a delay of around 40 days in the expulsion of the ejecta from the central binary. Moreover, we infer a relatively small (a few times 10$^{-6}$ Msun) ejecta mass ahead of the shock, considerably lower than the mass of 10$^4$ K gas inferred from radio observations. Finally, we infer that the dominant X-ray shock was likely not radiative at the time of our observations, and that the shock power was considerably higher than the observed X-ray luminosity. It is unclear why high X-ray luminosity, closer to the inferred shock power, is never seen in novae at early times, when the shock is expected to have high enough density to be radiative.