It does, considering the massive cultural impact China had on Japan. Where do you think buddhism, confucianism, black ink painting or their writing system comes from? Where do you think the literary references come from in a country that only had a writing system since the 8th century? Obviously, they had 13 centuries to integrate and create their own idiosyncrasies into all this imported chinese culture (and they did a pretty good work in many ways as some argue Japan invented the modern novels with the Tale of Genji and there is a good argument to be made for the invention of pop culture with woodblock prints of actors and wrestlers), but the chinese influence is still there in some tropes and I'll argue transvestism is one of them.