There is nothing magical, no marketing sham involved with microfiber cloths. Your issue is the material that is on your screen that doesn't belong there.
Water will never fully dissolve or remove oils. Oil and water.. cliche for a reason. If that is the type of stuff getting on your screen, you may have to do like I do (with a 2yr old) and use a actual screen cleaning product.
Sony S5100 BD-Player
Sony HT-XT1 Sound Base