That's not an accurate description what Bolukbasi et al (2016) [0] did. In particular, they do not list x close to lovely + he - she and then pick arbitrarily from that list. Instead, they explicitly reject that approach (see appendix A), because they're looking for pairs of words that are maximally gendered. They do that by finding x and y such that the angle between x - y and she - he is minimized. Since the task they're solving is different, you can't fault them for getting different results.
In the "King" example, you're adding and subtracting two words that are probably very close already, so if you want to find "something else" besides itself, you need to exclude it. For some problems it might make sense, for some others it might not.