I would be surprised if this result held up. Consider that the overall effect size is very small - the point estimate risk of a specific type of cancer (breast cancer) increased by 5% (alternatively: by a factor of 1.05) and was barely significant at the 95% level of confidence. Consider that data dredging indicated that the effect only held for a) pre-menopausal women who b) were smokers or had previously smoked. Dredging of this sort is not generally a good sign.
Most importantly, consider that the measure of light exposure was, in effect, an average over $1 \text{km}^2$, which hardly makes it accurate at the house-specific level that would be desirable. One suspects that northern or southern window exposure alone would make quite a bit of difference to nighttime light (the moon, for example) in some locales. On the Bortle scale, suburban nighttime light is about equivalent to a half moon. Sleeping with window shades drawn or not would make a huge difference in light exposure, and is not accounted for in the study. The actual measure used probably better represents a gradient of "urban - suburban - rural" living than the real light exposure the individual experienced. And, once one thinks about it that way, clearly there are lots of potentially carcinogenic effects correlated with urban - suburban - rural living that have nothing to do with nighttime light exposure, effects that have not been accounted for in the study.
To sum it up: large sample size with a barely significant result and a small effect size that is driven by a sub-population, combined with an independent variable that is likely to be poorly correlated with the variable of interest (in effect, it's an instrumental variable) but appear to be much more strongly correlated with other effects that are not accounted for, leads me to doubt the results are meaningful.