Earlier quoted context omitted.
The music and films are a big part of what conveys the American way of thinking about the world surely? I'll only genuinely start worrying about the Americanisation of world if the US somehow starts successfully exporting its insane attitudes towards guns, women's bodies and universal healthcare. Oh, and imperial units...
The US has managed to export significant parts of its political discourse in places where it makes no sense to have those discussions, simply by controlling global news. I think you underestimate how much this is.
The actual way this gets exported is via the HR firms and executive picks of American corporations. That then affects the funding of movies, TV shows, video games and everything downstream of that.