Your question is whether it's okay to call a male human being "a drama king(Q1)" or "a drama queen**(Q2)**."

The answer is yes. By extension, the expression "drama queen**(Q2)**" can be used regardless of gender. 

https://english.dict.naver.com/english-dictionary/#/entry/enen/039676b8ea084a81824b5f4719ea9a23

And a 'drama king' is a male version of a "drama queen".

https://english.dict.naver.com/english-dictionary/#/search?query=drama%20king

The word king is for a man and queen for a woman.