An Aesop: Never cheat at games. Even if it helps you win, it's never as satisfying as winning fairly.
Winning at games isn't nearly as important as having fun at games.
Benevolent Boss: The Magistrate wants to join in the Harvest Festival Games alongside Reader, despite that the latter is anxious that he can't win at these games. When Reader voices how inadequate he feels at winning these games for his boss, the Magistrate advises that winning isn't as important as enjoying the game.
Cheaters Never Prosper: Played with. Dongwa tries to play dirty by keeping Sagwa up all night so she'll be too tired, but it ends up backfiring when he loses even more sleep than she does. And even when he does win the race by cheating some more, he later admits to Sagwa that winning didn't feel as good as he hoped it would, because he didn't really win fairly.
What You Are in the Dark: Towards the ending portion of the episode, Dongwa exemplifies this twice.
During the race, Dongwa decides to cut corners by taking a shortcut. On top of that, he trips up Sagwa in order to get ahead of her, and wins the race. While nobody saw him take the shortcut, Sagwa is angry that Dongwa cheated his way into victory. Even though Dongwa points out his cheating still won him the title of fastest racer, Sagwa isn't impressed.
Later, when nobody else is around, Dongwa awards his prize to Sagwa, admitting he doesn't deserve it as much as her. He tells her that although it felt good to win at first, he realized it didn't feel gratifying since he cheated.
Brutal Honesty: Sagwa is told to make a painting of the Magistrate's "new outfit" when she sees nothing. Despite worrying that she'll be kicked out for being deemed foolish, she chooses to draw what she sees: that is, him in his underwear. Her honesty pays off, though, since the Magistrate deduces that Sagwa can't be foolish as she's one of his smartest cats, and therefore that these clothes must be a sham.
Comically Missing the Point: When the Miao family listens in on the con-artists, they overhear them brag about their scam and how they get to live in the palace without really doing anything. Among the cats, Sheegwa wonders if this means they're all fools for being unable to see the robes.
Dramatically Missing the Point: The con-artists trick relies on this trope. Their trick relies on everyone to overlook the possibility that they can't see the invisible robes because they aren't there. Instead, everyone who looks upon the unseen "robes" thinks this means they're a fool. It takes Sagwa painting the Magistrate in his underwear for him to realize there are no robes. And it takes him voicing the truth for everyone else in his entire court to understand why they can't see the robes.
Good Parents: When Sagwa claims she's a fool for being unable to see the robes, Mama and Baba Miao make it a point to tell Sagwa she's very bright and, rather, there's something wrong with the robes istead. They have such faith that their daughter is not only being honest, but her seeing no robes despite being intelligent must contradict the robes' ability to detect fools.
Irony: The Con artists actually do know how to sew and weave. The irony of it all is, they could've honestly offered their services as plain old seamstresses, and they might've gotten further in life than try to lie their way into an easy life in the palace.
Laser-Guided Karma: For trying to scam their way into a cushy life in the palace, the con artists (who indeed can sew and weave) are to not only pay a fine equal to what they were commissioned, but also tasked with sewing new outfits for the Magistrate and his family and his servants and the Miao family.
O.O.C. Is Serious Business: The Foolish Magistrate is, true to his namesake, not always the brightest character in the show. If he's the first to recognize Sagwa's painting means there are no robes and he's the voice of reason, then it means the con-artists have been caught red-handed.
Spanner in the Works: If Sagwa hadn't told her parents about being unable to see the new robes, her family might not have suspected that something was up.
