There is no such thing as another kind of soft power.  It is not soft power when you can't positively influence other people who are not like you because they can't relate with you.  The West had it easy because their media permeated the whole world and Western culture is seen as superior by most people in the world for centuries.  Western media is the default media for the world.  

Soft power has to come from the creative and artistic people.  They do things from the heart and it will resonate with other people in the world.  To overcome the overwhelming Western soft power monopoly, China needs to look at how Korea and Japan were able to win over the world.  People are learning Japanese and Korean because of that.  The need to show you are cool is very important instead of perpetuating the communist imagery propogandized by the West.