Two-Higgs-Doublet Model of Type-X in the large tan⁡β limit becomes leptophilic to allow a light pseudo-scalar A and thus provides an explanation of the muon g−2 anomaly. Introducing a singlet scalar dark matter S in this context, one finds that two important dark matter properties, nucleonic scattering and self-annihilation, are featured separately by individual couplings of dark matter to the two Higgs doublets. While one of the two couplings is strongly constrained by direct detection experiments, the other remains free to be adjusted for the relic density mainly through the process SS→AA. This leads to the 4τ final states which can be probed by galactic gamma ray detections. © 2018 The Authors