Yes, cats’ eyes really do reflect light, and there are a couple of reasons why. One is that they have a reflective layer, the tapetum, within the eye that intensifies any light coming in.
Couple that with the fact that in a low-light situation the cat’s pupils are dilated enormously, and you are, in effect, looking into two small mirrors when you look at your cat’s eyes. Some humans seem to have eyes that are more reflective than normal, and we often say that such a person has “cat eyes.”