I have been playing Ryze for a long time, and tried to create different playing styles for him. In this season, many new items really suit Ryze especially the upgraded version of Manamune - Muramana.
This item made Ryze become an insane single target assasin because he can takedown a non-tank target in less than 3 seconds, really. On the other hand, NO ONE can beat you in a 1v1 fight if you two are on the same level, neither they can escape from you.
Though there are many ways to play Ryze, I think this is unique and op as well as it is hard to control. It makes you not only do damages in spells but also with auto attacks, at the same time you are tankier than other mages and have a little bit more cc and surviving ability than the original Ryze.