We report on real-time measurements of the crystallization process of highly ordered thin films of the molecular organic radical p-nitrophenyl nitronyl nitroxide (p-NPNN) grown from the vapor phase on glass substrates. The films exhibit 2D spherulitic morphology with a low density of nucleation centers. This low density allows an accurate determination of the time evolution of the spherulites radii, which show a non-linear dependence with time. The non-linearity is more pronounced for small values of the film thickness and is due to the non-negligible contribution of the interfacial energies at the beginning of the crystallization process. As time evolves the film thickness increases and the dependence becomes nearly linear (in-plane growth rate almost constant).