Twisting a van der Waals bilayer changes not only the moiré periodicity but also the local stacking and interlayer hybridization. Here, we show, using fully relaxed first-principles calculations including spin–orbit coupling, band unfolding, and Brillouin-zone-integrated densities of states, that bilayer PtTe₂ exhibits a non-monotonic evolution between gapless and gapped electronic regimes. The 7.34^∘ structure remains gapless, whereas finite direct gaps appear at the sampled intermediate angles. The gap closes at the sampled 60^∘ configuration and reopens at higher angles. The direct gap shows an overall increase with the minimum local interlayer Pt–Pt separation, although the complete distribution of local stacking environments is required to account for deviations from this trend. At 7.34^∘, the low-energy states are concentrated predominantly in the AA-like regions of the otherwise gapless moiré cell. Controlled interlayer-separation scans show that increasing the layer spacing removes the near-E_F crossings and opens a gap, consistent with weakened interlayer Te-p_z hybridization. These results identify the redistribution of interlayer hybridization as the microscopic origin of the re-entrant gap evolution in twisted bilayer PtTe₂.