Not sure about the cultural dig at the English (that was probably very context-dependent and an in-joke for Germans/German speakers). But in general, Nietzsche probably meant something like "Man strives for power" by which he might have meant something more like self-expression that raw physical or political power.

I would personally say that most people strive for meaning (as in, living a meaningful life) even if they think they are striving for "happiness", which to me comes off as a very shallow and hedonistic aim.