Mike Pence's remark shows threat against People's Republic of China. But, China's intention to export its political mindset has been observed for more than 3 years such as sudden expansion of Confucious Institutes around the world. Basically, the institutes are just educational institute teaching Chinese Language and Cultures. But, judging from the situation that political discussion and criticism against Chinese government are prohibited, they seem to be monitored by Chinese Communist Party to an extent.
(I don't reject education of the Chinese Language and Cultures. I just think it should be taught under internal carriculum in each university)
The problem is not only international relationship but also domestic political issue. Constitutional revision there in 2018 fixed Xi Jing Ping as the eternal president. It means the country revived emperor system in fact. It's complete decline of democracy in China.
I guess it's too late that American politician noticed it.