We evaluate the phase diagram of the four-site Kern-Frenkel patchy particle model [Kern, N.; Frenkel, D. J. Chem. Phys. 2003, 118, 9882.], a model representative of particles interacting via short-range orientational interactions, for several values of the interaction range. Similar to what has been found for isotropic potentials, the liquid phase disappears as an equilibrium phase for values of the range on the order of 15% of the particle diameter. For smaller ranges, the gas-liquid phase separation becomes metastable with respect to crystallization into a diamond-like structure. Interestingly, and differently from the isotropic case, the supersaturation of the fluid at the critical point does not significantly increase upon going toward the adhesive (vanishing interaction range) limit.