Cross-over stocks are not uncommon on shotguns, where most shooters keep both eyes open to successfully hit flying/moving targets. If there is no clear eye-dominance, or the left-eye is dominant but the shooter 'right-handed', then the cross-over stock is a big advantage.

On a rifle though, injury to the right eye is about the only explanation, as DD says. If the left-eye was dominant, it could simply be closed, or at the very least 'squinted', to change dominance back to the right eye to align the sights on a straight-stocked rifle.