Accurately modeling gas-surface collision dynamics presents a great challenge for theory, especially in the low-energy (or temperature) regime where quantum effects are important. Here, a path integral-based nonequilibrium ring polymer molecular dynamics (NE-RPMD) approach is adapted to calculate dissociative initial sticking probabilities (S0) of H2 on Cu(111) and D2O on Ni(111), revealing the distinct quantum nature in the two benchmark surface reactions. NE-RPMD successfully captures quantum tunneling in H2 dissociation at very low energies, where the quasi-classical trajectory (QCT) method suddenly fails. Additionally, QCT substantially overestimates S0 of D2O because of severe zero point energy (ZPE) leakage, even at collision energies greater than the ZPE-corrected barrier. Instead, NE-RPMD predicts S0 values of D2O in much improved agreement with reference results obtained by the quantum wavepacket method with reasonable corrections of the thermal contribution. Our results suggest NE-RPMD as a promising approach to model quantum effects in gas-surface reactions.