We use multi-object near-infrared spectroscopy with VLT/KMOS to investigate the role of the environment in the evolution of the ionized gas properties of narrow-band-selected H α emitters (HAEs) in the Spiderweb protocluster at z = 2.16. Based on rest-frame optical emission lines, H α and [N II]λ6584, we confirm the cluster membership of 39 of our targets (i.e. 93 per cent success rate), and measure their star formation rates (SFR), gas-phase oxygen abundances, and effective radius. We parametrize the environment where our targets reside using local and global density indicators based on previous samples of spectroscopic and narrow-band cluster members. We find that star-forming galaxies embedded in the Spiderweb protocluster display SFRs compatible with those of the main sequence and morphologies comparable to those of late-type galaxies at z = 2.2 in the field. We also report a mild gas-phase metallicity enhancement (0.06 ± 0.03 dex) at intermediate stellar masses. Furthermore, we identify two UVJ-selected quiescent galaxies with residual H α-based star formation and find signs of extreme dust obscuration in a small sample of starbursty submillimetre galaxies based on their FIR and H α emission. Interestingly, the spatial distribution of these objects differs from the rest of HAEs, avoiding the protocluster core. Finally, we explore the gas fraction-gas metallicity diagram for seven galaxies with molecular gas masses measured by ATCA using CO(1-0). In the context of the gas-regulator model, our objects are consistent with relatively low mass-loading factors, suggesting lower outflow activity than field samples at the cosmic noon and thus, hinting at the onset of environmental effects in this massive protocluster.