Don't spoil your firstborn son.
This story was regarded as incredibly controversial in its day, because the core argument of the novel is that Gildong was the better son, excellent in every way, but because of some cultural rule, his father never gave him any approval or attention. Gildong left his father's house because he felt the rule about preferring the firstborn son was stupid and unjust. But that was a very common practice in human history, especially in the author's own context. Gildong is shown to be a fair king because he doesn't arbitrarily treat some people better than others.
Excellence, power, and nobility.
This novel is a pretty sophisticated depiction of a literary idea sometimes referred to as noblesse oblige, which is French for "The obligation of the nobility." The idea is that with great power comes great responsibility. In this story, Gildong is a hero specifically because he realizes how much privilege and advantage he has available to him, and he uses it to become a super hero to help other people. This is a picture of what noblesse oblige really means, that wealthy people have an obligation to help people who don't have as much. Notice that Gildong is so convinced about this point that he becomes a vigilante; when he finds greedy rich people, he robs them and gives all their money to the poor against their will.
Balance, fairness, and peace.
When Hong Gildong is exiled from his motherlands, he reforms his small militia of bandits again, called Hwalbindang, he goes back to stealing from the rich and giving to the poor, but when he comes into the land of Yul and begins visiting with the poor and needy there, he realizes that the kingdom itself is unjust because it is led by a bad king. He deposes that king, kills him, and becomes the king of Yul. His reign is known for its balance, fairness, and peace. These are the virtues that he treasures, since his own home life was filled with conflict and strife.