We consider a concise dark matter (DM) scenario in the context of a nonexotic U(1) extension of the Standard Model (SM), where a new U(1)(X) gauge symmetry is introduced along with three generations of right-handed neutrinos (RHNs) and a SM gauge singlet Higgs field. The model is a generalization of the minimal gauged U(1)(B-L) (baryon number minus lepton number) extension of the SM, in which the extra U(1)(X) gauge symmetry is expressed as a linear combination of the SM U(1)(Y) and U(1)(B-L) gauge symmetries. We introduce a Z(2)-parity and assign an odd-parity only for one RHN among all particles, so that this Z(2)-odd RHN plays the role of DM. The so-called minimal seesaw mechanism is implemented in this model with only two Z(2)-even RHNs. In this context, we investigate the physics of RHN DM, focusing on the case where this DM particle communicates with the SM particles through the U(1)(X) gauge boson (Z' boson). This "Z'-portal RHN DM" scenario is controlled by only three free parameters: the U(1)(X) gauge coupling (alpha X), the Z' boson mass (m(Z)'), and the U(1)(X) charge of the SM Higgs doublet (x(H)). We consider various phenomenological constraints to identify a phenomenologically viable parameter space. The most important constraints are the observed DM relic abundance and the latest LHC Run-2 results on the search for a narrow resonance with the dilepton final state. We find that these are complementary with each other and narrow the allowed parameter region, leading to the lower mass bound of m(Z)' greater than or similar to 2.7 TeV.