Zen and Yin-Yang come from different traditions — Buddhism and Taoism, respectively — but they share an emphasis on harmony and balance.
Yin and Yang is the Taoist principle that all things exist as a balance of opposing but complementary forces (e.g., light/dark, active/passive). Its importance lies in seeking harmony and recognizing that these opposites are interconnected parts of a single whole.
Zen is a Buddhist practice focused on achieving enlightenment through meditation and mindfulness. Its importance is in transcending dualistic thinking (e.g., good/bad, right/wrong) to experience reality directly. Their connection lies in how the Taoist idea of Yin-Yang helped explain Zen's goal. The concept of balancing interdependent opposites resonates with the Zen pursuit of a "Middle Way" and understanding that seemingly separate things are ultimately unified.
Once you complete the game you can try to manipulate it to achieve balance or have Yin or Yang dominate.