It was a charity game played by Korean celebrities. The silly part where they get on one leg and bump into each other is called 닭싸움 or "chicken fight". It's a children's game. The goal is to knock your opponent off balance using only your protruding knee, and whoever falls or drops their leg loses.

They're basically parodying the usual baseball fight where both teams mob the field and start pounding on each other. It's all in lighthearted fun. Many of my childhood disputes were also settled this way.