The atmospheric neutrino-oxygen neutral-current quasielasatic (NCQE) reactions are one of the main background in the search for supernova relic neutrinos. Here, we report the first measurement of the atmospheric neutrino-oxygen NCQE cross section in the Super-Kamiokande Gadolinium (SK-Gd) experiment using 552.2 days of full SK-VI data. The measured NCQE cross section is 0.74 ± 0.22(stat.) +0.86/-0.16(syst.) × 10^(-38) cm^(2), which is consistent with the theoretical NCQE cross section and the previous study in SK within the range of the uncertainty. Furthermore, we established the verification method for nucleon-nucleus interaction models using atmospheric neutrino events. We performed the verification using the Bertini Cascade model (BERT), the Binary Cascade model (BIC) and the Liège Intranuclear Cascade model (INCL++). As a result, we suggested that BIC and INCL++ are closer to the observed data.