They didn't take it over "forcibly", they took it over with popular support from the Chinese people. If that doesn't grant you legitimacy I honestly don't know what would.
Popular support would be democratic elections. That's not what happened - it was a civil war, fighting the KMT supporters.
The reason it had popular support is because USSR gave them money and resources, presumably just for this reason.
The Qing Dynasty lost Formosa to Imperial Japan in 1895.
Formosa wasn't a part of China in the 1930s it was a part of Japan.