Energy is non-matter. Matter/energy interaction is not a mystery.
Now if you want an example of something using something that is not-matter, then I propose that all examples of Microsoft Windows be destroyed except for one compressed, encoded file. That one encoded file is beamed, using any frequency you wish and compatible with transmission, at any remote galaxy. Upon completion of the transmission the remaining file is erased along with the decoding key. Does Microsoft windows exist?
That's news to me. I could have sworn matter and energy are interchangable and that there was a famous formula defining the equivalence.
Now about the little windows thought experiment. Does a text exist if the only copy of it resides in the form of an unbreakable cipher, for which the key is lost? I would argue that this is equivalent asking if a flammable object exists after it is burned. If an object cannot be reassembled, it does not exist, at least not in any usual sense. If the hypothetical message can be decrypted, then it exists.