"On the part of" is an idiomatic expression for something that is done by someone or something. Normally there is an extra "the" in there. "Good on the part of Taiwan" just means "Taiwan did something good." It doesn't have anything to do with Taipei being a part of Taiwan. They could have also said "Good on the part of Taipei" or "Good on Taipei's part."

https://dictionary.cambridge.org/zht/%E8%A9%9E%E5%85%B8/%E8%8B%B1%E8%AA%9E-%E6%BC%A2%E8%AA%9E-%E7%B9%81%E9%AB%94/on-the-part-of-sb-on-sb-s-part