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.
That said, if your conversation partner doesn't understand what you say, be conventional: oldie but a goodie.