If you look at the period from 1945 to, say, 1975, though, which is the speaker's perspective, American political and economic influence were both extremely strong compared to today, in addition to the obvious military influence.
Not only then, but still today. (If not even more today.) I remember the late unpleasantness with the PIIGs, and believe it or not, there was a little while there where people would try to determine where a Euro note came from...
and they wouldn't take it unless it was from Germany.
The Germans may not be vocal about dominating Europe, but they definitely dominate Europe. And they have in many ways for a long time. At least since the 60's.