The shock-induced combustion ramjet (Shcramjet) based on oblique detonation waves (ODWs) is among the promising choices for hypersonic propulsion systems. An understanding of the ignition, propagation, and stability of ODWs is critical to harnessing their propulsive potential. In such high speed reacting flows, there is a high probability of occurrence of non-thermal reactions due to the presence of non-trivial amounts of highly reactive radicals including H, O and OH apart from O2 as demonstrated recently [M. P. Burke, S. J. Klippenstein, Nat. Chem. 9 (2017) 1078–1082, Y. Tao, A. W. Jasper, Y. Georgievskii, S. J. Klippenstein, R. Sivaramakrishnan, Proc. Combust. Inst. 38 (2021) 515–522]. The present work focuses on examining the initiation, propagation and structure of oblique detonation waves in stoichiometric H2-air mixtures through numerical simulations with and without non-thermal reactivity on a two-dimensional adaptive grid. Non-thermal reactions were included in the macroscopic kinetic model as chemically termolecular reactions facilitated by the H + OH radical-radical recombination and the H + O2 radical-molecule association reactions. Since, the non-thermal reactions result in a corresponding decrease in the reaction fluxes of the incipient recombination/association reactions, an additional simulation was performed by applying corrections to the respective incipient recombination/association rate constants using the methodology demonstrated by Tao et al. [Y. Tao, A. W. Jasper, Y. Georgievskii, S. J. Klippenstein, R. Sivaramakrishnan, Proc. Combust. Inst. 38 (2021) 515–522]. Results show that, under ODWE relevant conditions, non-thermal reactivity fundamentally alters the induction length, intensity as well as the structure of the ODW. Specifically, it is found that non-thermal reactivity leads to a noticeable reduction in initiation length and a simultaneous increase in instantaneous peak heat release rate and the degree of unsteadiness of the ODW. Statistical analysis of key thermo-chemical variables is performed to elucidate the important species as well as reactions responsible for the observed variations.