Tl;dw - Unlike China and Japan, medieval Korea followed an extreme school of Confucianism that emphasized hierarchy and age over practicality. After WW2, the South Korean ~~dictatorship~~ government used this tradition to cement their own power. The video argues that these have made South Korea an extremely hierarchical, and in particular, sexist, society. A video game's refusal to sexualize a female character for their (mostly male) audience was thus seen as an attack on the system. A female artist at the studio was accused of being a 'radical feminist', and either fired or resigned to appease fans.
Edit: As Denjin pointed out, it should be Ming Dynasty and not Tang Dynasty.
You need to watch at least the start of the first video.