I wanted to provide a counter point, or rather, a more balanced and self-conscious vision. As to your definition of what "third world" meant, that's not how I remember it (but I grew up in West Germany, and the GDR may have defined terms differently). The "third world", according to the Western definition, definitely were those countries that were poor (and also perceived as primitive and culturally backwards, so the term eventually came to be seen as stigmatizing, at least with left-leaning people).
What you're referring to, the unaligned countries/states, were called "blockfreie Staaten", and they were not "promoted" in Western propaganda as featuring "despots", but still could end up being bombed (democratically), like founder state Yugoslaviya.
But it is also true that many "third world" countries joined the block-free group, so there is considerable overlap.