Because Puyi was no longer Emperor of China as of the Xinhai Revolution in 1911. The Qing Dynasty was no longer the recognised legitimate entity of China. During the Japanese invasion, the leader of the Republic of China was generally recognised as Chiang Kai-shek. Puyi was Emperor of Manchukuo, the puppet state controlled by Japan, with the promise that he would be Emperor of China again. It didn't happen.
China was also never fully controlled by Japan.
Technically, most people would agree that Chiang Kai-shek was the one running the show. However, he had made some people unhappy by arresting
some important guy, and thus decided to "resign" so as to avoid needless unrest in the middle of the Japanese invasion of Manchuria. In his place was now Lin Sen, an old man who was respected, but in the end taking orders from Chiang Kai-shek. Lin Sen would be the Chairman of the National Government of the Republic of China between 1931 and his death in 1943 (car accident).
This is why in HoI3, the leader of ROC in the 1936, 1939 and 1941 bookmarks is Lin Sen, and I would suspect he is the leader of ROC also in HoI4.