To be fair, the UK is also a cultural giant with respect to radio(!), TV, film, and music. But yes, your point about culture exports is the key to understanding why English is so frequently someone's second language.

> English has been adopted as the international language (largely thanks to American TV, Movie and Music exports)

The British Empire might have had something to do with it too...

I doubt it: it lost its importance before English was established as the world language. E.g., German was still the international scientific language in the early 1900s. And let's not kid ourselves and believe that European countries would have adopted English because it's spoken in, say, India. If sheer numbers were the defining factor, we'd all have adopted some standard Chinese a long time ago.