**Abstract** : The effect of the relativistic treatment of two-body reaction kinematics on atomic recoil energy and subsequent primary damage parameters, such as damage energy and number of atomic displacements, has been studied. If the emitted particle has a mass larger than the incident particle, the ratios of relativistic quantities in comparison to the classic mechanical ones can be null and infinite due to the null recoil energies. However, the relativistic corrections on recoil energies are limited in [-0.6%, 0.5%] and [-6%, 5%] for 20 MeV and 200 MeV neutron discrete (n, $\alpha$) reactions of $^{56}$Fe. For (n,n') and (n,p) reactions of any nucleus, the relativistic corrections are about 1% on recoil energy for a 20 MeV incident neutron, while the corrections can be more than 30% (about 10% on average) for 200 MeV incident energy. The relativistic effect is less than 5% on ($\alpha$,n) reaction inducing recoil energy of any nucleus (and within 0.6% on atomic displacement damage for $^{56}$Fe) for secondary energy lower than the incident energy of 200 MeV. On the other hand, about 10 keV and 1500 keV broader Primary Knock-on Atom (PKA) spectra are respectively found for 20 MeV and 200 MeV neutron-induced (n,n'), (n,p), and (n, $\alpha$) reactions of $^{56}$Fe. Therefore, the relativistic treatment of two-body reactions should be applied for computing PKA spectra and subsequent radiation damage for high energy neutrons.