It is an interesting perspective
Edited for accuracy, 'cultural' -> 'communist'
The cultural revolution took place well after the CCP took over.
Not the Cultural Revolution. Cultural Revolution was in the 1960s, the Communist victory over the Nationalists and the Nationalists' flight to Taiwan was late 1940s. The "Cultural Revolution" was not a "revolution" in the classic sense. It was not an attempt to install a new government. It was a totalitarian exercise in which the Communist Party – led by Mao – attempted to eliminate every aspect of Chinese culture and society that wasn't enthusiastically communist
Incorrect. The previous government of China (the Beiyang government) was overthrown by a collaboration between the CPC and the KMT (Which was led by Chiang Kai-shek).
The CPC and the KMT then had a war, which the KMT lost - and fled to Taiwan.
As a bonus, the KMT then proceeded to carry out the White Terror - 38 years of one-party rule, repression and martial law, which ostensibly purged Taiwan's of suspected or alleged communists.