Something like this website doesn't teach you vim, it teaches you vi keybindings and the basic concepts. Vim bindings are available in all the editors you mentioned (although my understanding is that the Notepad++ bindings in particular are bad). For the people who say they're using vim productively, they're usually running some combination of plugins (that hopefully don't step on each others toes) that emulate the featureset of an IDE that they want to use.

And you're bang on wrt nano existing everywhere vim does!