We revisit the case of scalar dark matter interacting just gravitationally with the Standard Model (SM) particles in an extra-dimensional Randall-Sundrum scenario. We assume that both, the dark matter and the Standard Model, are localized in the TeV brane and only interact via gravitational mediators, namely the graviton Kaluza-Klein modes and the radion. We analyze in detail the dark matter annihilation channel into two on-shell KK-gravitons, and contrary to previous studies which overlooked this process, we find that it is possible to obtain the correct relic abundance for dark matter masses in the range [1, 10] TeV even after taking into account the strong bounds from LHC Run II. We also consider the impact of the radion contribution (virtual exchange leading to SM final states as well as on-shell production), which does not significantly change our results. Quite interestingly, a sizeable part of the currently allowed parameter space could be tested by LHC Run III and by the High-Luminosity LHC. arXiv:1907.04340v1 [hep-ph] 9 Jul 2019 of how dark matter can be included within this hypothesis; in Sec.3 we show our results for the annihilation cross-sections of scalar DM particles into SM particles, KK-gravitons and/or radions; in Sec.4 we review the present experimental bounds on the Kaluza-Klein graviton mass from LEP and LHC, as well as on the DM mass from direct and indirect search experiments, and we remind the theoretical constraints coming from unitarity violation and effective field theory consistency; in Sec.5 we explore the allowed parameter space such that the correct relic abundance is achieved for scalar DM particles; and, eventually, in Sec.6 we conclude. In the Appendices we give some of the mathematical expressions used in the paper: App. A contains the KK-graviton propagator and polarization tensor; in App. B we provide the Feynman rules for our model; in App. C we give the expressions for the decay amplitudes of the KK-graviton and of the radion; and, eventually, in App. D we give the formulae for the annihilation cross-sections of dark matter particles into Standard Model particles, KK-gravitons and radions.