I can't say for certain, but here's my two cents on what I think happened:
Kubo's magic throughout the movie has been based around the power of storytelling, of making people invested in something that isn't there. The Moon King has spent the whole movie trying to get Kubo to effectively relinquish his mortality and become an immortal, non-temporal being with no need or care for the concept of remembering things through stories. When the Moon King is mocking Kubo about how everything he's ever valued is gone forever, Kubo realises that no, the Moon King is wrong — with the power of remembrance by way of storytelling, he and other mortals can still have a connection with those they have lost. Kubo summons the spirits/memories of the dead to prove his point. Ultimately, this form of magic is so antithetical to the Moon King's very worldview that clashing with it effectively destroys him. What's left is only a husk of what the Moon King might perhaps have been like before he relinquished his own mortality/temporality in the way he wanted Kubo to do.
I realize this sequence of events isn't very logical, but I feel like it makes a degree of emotional sense which, as I mentioned on the Disney thread, is what I think the movie was going for. Hence, I don't have a problem with it, although I can see why some might. Ultimately, I do think it's a more satisfying way to off the villain than just having Kubo brute force him to death. It's also in service to a pretty decent moral about accepting what you've lost can still be retained in some form by carrying on their stories — an aesop that, refreshingly, isn't undermined by just having Kubo's parents return to life afterwards.
Makes better sense, I guess.
Wasn’t hoping Kubo would kill him either. I appreciate the aversion, but the execution was unclear.
edited 11th Dec '17 11:17:01 PM by Tuckerscreator
So he did change his mind. But it seems unclear why, and how he knew this song would work.