빛나다 is giving off light, or of a person, being radiant. -게 supplies the kind of shine: 밝게 빛나는 (shining brightly, in two lines), 찬란하게 빛났다 (shone brilliantly), 영롱하게 빛나고 있는 (glowing lustrously). It applies as readily to food and objects under studio lights as to people — 그렇게 빛나는 여자 is a woman who shines.
Register: several lines are caption-style and lyrical