I've also seen Triumph of the Nerds, and it glosses over many things, attributes many things to Apple and Microsoft that shouldn't be, or at least they merely shared in bringing these things about along with other companies, etc. If your only source of information is that documentary I highly recommend digging a bit more. One of the very first video game companies, and a very successful one, for example was Adventure International. And that companies first products were for the TRS-80; not the Apple II.
Stargunner, you're about spot on with your post except that in Europe it went from CP/M for business to the PET and then to DOS. The PET was huge in Europe for business, though failed spectacularly in the U.S.