The heat transfer properties of the organic molecular crystal α-RDX were studied using three phonon scattering based thermal conductivity models. It was found that the widely used Peierls-Boltzmann model for thermal transport in crystalline materials breaks down for α-RDX. We show this breakdown is due to a large degree of anharmonicity that leads to a dominance of diffusive-like carriers. Despite being developed for disordered systems, the Allen-Feldman theory for thermal conductivity actually gives the best description of thermal transport. This is likely because diffusive carriers contribute to over 95% of the thermal conductivity in α-RDX. The dominance of diffusive carriers is larger than previously observed in other fully ordered crystalline systems. These results indicate that van der Waals bonded organic crystalline solids conduct heat in a manner more akin to amorphous materials than simple atomic crystals.