Do you think The Night’s King on the show has anything to do with The Night’s King from the books? My interpretation of the book character is that he made common cause with The Others, but he was never their equal, let alone their leader: he was their slave.

Basically, nothing but the name. The Night’s King in the books was a human being and not a White Walker, and he had a very particular story of hubris, temptation, tyranny, and overthrow that the enigmatic figure in the show completely lacks. 

However, I think it is absolutely vaulting past the evidence to say that he was the slave of the White Walkers. Rather, he seems to have been some form of ally, marrying into the family with his corpse queen, and engaging in some form of religious communion via human sacrifice.