AFAIK, England's parliament, prior to the US, could not remotely be described as a democracy. Indeed, it was well over a hundred years later that this would be the case.
I have no idea what he means by "other parts of Europe". My best guess would be San Marino, which has had a democratic-ish thing going for a very long time. But San Marino was (and indeed is) pretty far from a modern democracy in any sense of the term.
The US might not have a lot of things going for it. But I think it's fair to say that it's the first modern democracy.