The other reason to not exclude King is that it's pretty likely that Queen is the closest word to King. Then King - X + Y = Queen is just saying that X and Y are close to each other, not an interesting result.
From my perspective (linguistic anthropology), they’re not actually all that close. Most historical “queens” (which have that label applied to them by modern English speakers) were not rulers (and we have a separate term, “queen regnant”, for that) but rather the gender dual to the male “royal consort.” It was only in recent history where you see examples of “equal-opportunity” monarchies that could have either a male or female monarch of equal power, and thus usages of “queen” to denote those monarchs.
Thus—given that we’re defining words based on their centroids of usage in a historical corpus—if a woman is a monarch of a kingdom, “king” is a tighter historical fit to describe her role than “queen” is.
Luckily we don't have to speculate. See a web interface at [1]. Select English from the dropdown and it says that the closest word to king is kings and second is queen, then monarch. And to test my second statement I also tried "red is to king as blue is to ___" and got kings and queen as the top two answers.
Considering the very high dimensionality of the space, it's not as obvious as you think. Consider the noise inherent in the word 2vec negative sampling method as well. Another word could very well end up closer to "king".
