The motif of human value
Many features of Hong Gildong point to the hero's mistreatment at his father's house. He steals from the rich to give to the poor, because he believes the rich are not doing their duty to keep the nation thriving. Why? Because they don't value the lives of the poor. Also, he is passionate about second-born sons getting treated fairly, instead of spoiling the firstborn which tends to make one spoiled kid and one bitter kid. Hong Gildong is defined by his consistent empathy, because he treats all people as if they are equal.
The royal motif
Gildong is half royal, because his dad holds an important political office that would likely be passed to Gildong, except that he is the second-born, so the power will transfer to Gildong's older brother. But that doesn't mean that Gildong is not a king. Throughout the story, he leads an army of ragtag vigilantes, and when he establishes his government in Yul, everyone claims he is a great king. This royalty motif makes the story more mythic, and it shows that Gildong is an example for honorable behavior.
The symbolic theft from the rich
It isn't clear that Gildong even considers his gang's actions to be criminal. He seems to feel that he is behaving according to unspoken moral guidelines that explain themselves. That means that when he steals, it's symbolic. It represents that crime is a natural by-product of systemic injustice for one thing, but in a more abstract way, it also represents karmic justice. By being greedy, the rich have invited their own doom, in Gildong's opinion.
The symbolic assassination
When Gildong is attacked by the invador who was hired to kill him, he masterfully defends himself and kills the assailant. This symbolized his importance as a person, of course, but it also signifies his responsibility, because it proves he can take care of himself. Compare that to his spoiled older brother who has never had to fend for himself, and it becomes clear what this represents. It represents that Gildong is correct that second-born sons are equally competent, if not more competent.
The deposition of the king of Yul
When the king of Yul is deposed of his throne by Gildong, he represents the old fashioned social order that dominated Korea at the time. When the vigilante hero arrives to Yul, the people of the kingdom are suffering because the king was greedy with his wealth, and because he was capricious. Gildong's assassination of the king represents that his point of view is stronger than the traditional opinion. He is a better king, too.