Enigmatically means in a mysterious way — in the manner of something hard to read. Someone may smile enigmatically, or answer enigmatically, so you cannot tell what they really think. It is just enigmatic with -ally on the end, to talk about how something is done, not what it is. It is not a word for everyday chat; in a mysterious way is what most people say. Use it when you want that slightly story-like feel. It does not mean the thing was enjoyable, and it does not mean you liked the mystery. It only describes the manner.