This doesn't make sense to me. The iris doesn't collect light for vision. The pupil expands or contracts to vary the amount of light that reaches the retina. Iris color should have nothing to do with it.
From the first source on the linked study, they describe it as the following:
(...) This functions as a mirror providing the second opportunity for photon capture by reflecting light back through the retina, enhancing visual sensitivity.
Most reindeer live North of the Arctic Circle, where the sun does not rise above the horizon in winter months.
I suspect most summer days are brighter than the few hours of twilight the reideer get in December.
A lighter iris color correlates with higher light sensitivity and better low light vision. The higher density of pigment in a darker iris blocks light better.