It seems this blue ginger is perfectly safe to eat, because I've eaten plenty of it and been fine. I eat ginger just about every day. It's a wonderful panacea remedy; I mainly use it to promote better digestion and to get rid of indigestion from over-eating and hard-to-digest foods like beef and saturated fats.
It's definitely not chlorophyll because ginger's flesh is from the plant's rhizome which grows well beneath the soil; too deep for light to penetrate. Also, the leaves are where most of the chlorophyll production happens, even the lower stems are almost pure white in color. Although there is a layer of beautiful purple coloration just above the soil line on most ginger plants, the blue ginger most certainly seems like a different type of ginger; possibly a sub-species.
As a ginger connoisseur of sorts, I find this fine to eat, but I most definitely prefer the taste of the yellow ginger, and especially the white ginger (which is juicy, mild, & delicious) varieties better than the blue stuff. Hope that adds some useful info to this thread.