We present a parallel implementation to compute electron spin resonance g-tensors at the coupled-cluster singles and doubles (CCSD) level which employs the ACES III domain-specific software tools for scalable parallel programming, i.e., the super instruction architecture language and processor (SIAL and SIP), respectively. A unique feature of the present implementation is the exact (not approximated) inclusion of the five one- and two-particle contributions to the g-tensor [i.e., the mass correction, one- and two-particle paramagnetic spin-orbit, and one- and two-particle diamagnetic spin-orbit terms]. Like in a previous implementation with effective one-electron operators [J. Gauss et al., J. Phys. Chem. A 113, 11541-11549 (2009)], our implementation utilizes analytic CC second derivatives and, therefore, classifies as a true CC linear-response treatment. Therefore, our implementation can unambiguously appraise the accuracy of less costly effective one-particle schemes and provide a rationale for their widespread use. We have considered a large selection of radicals used previously for benchmarking purposes including those studied in earlier work and conclude that at the CCSD level, the effective one-particle scheme satisfactorily captures the two-particle effects less costly than the rigorous two-particle scheme. With respect to the performance of density functional theory (DFT), we note that results obtained with the B3LYP functional exhibit the best agreement with our CCSD results. However, in general, the CCSD results agree better with the experimental data than the best DFT/B3LYP results, although in most cases within the rather large experimental error bars.