Sure they do. They just do it through second-order effects so it seems less obvious what's going on. I recall an instance where an American basketball team owner said something in support of the Hong Kong protests. His team was immediately banned from China, both physically and via broadcast.

Being able to publicly censor foreigners who dislike your policies is a useful power.

When you control economic access to a billion people, you don't always need guns to get others to do that you want. (China does have plenty of those guns, though, if and when they decide they need them.)