How relevant should the links be? The first 4 are all about Japan. The fifth is about an empire that heavily influenced Japan (especially the Tang Dynasty, I believe). The Mongols never captured Japan, which fought them off. Korea has had a long and uneasy relationship with Japan.
I think I'd ask you all: If this article were about English history, would you suggest to see also an article on French history because the Normans once occupied England and the English used to occupy much of France? Would you suggest an article on German history because the British fought off the Nazis (much as the Japanese fought off the Mongols)? Would you suggest an article on the history of the Netherlands, because of an extensive history of trade and competition for colonies, or Italy, because of the longtime English love affair with Italy that goes back to at least the 16th century? Would you suggest an article on the history of Spain, because of colonial competition?
Depending on how you answer those questions, it may become clear how we should handle articles about the histories of neighboring and not so neighboring countries.
As for me, I would keep the Chinese Empire article in the list, but I'd immediately delete Mongol Empire. I'm not sure about Pre-modern Korea, which to my mind would be somewhat analogous to a comparable article about French history in an article about English — or maybe better, German — history. Ikan Kekek (talk) 07:02, 21 May 2016 (UTC)