Thanks for the thoughtful response! I think I might want to rephrase the first part of my question. I get that it's not so much a pass/fail set of criteria as it is a design intent. However, the threads that have been outlined here that tie Dream Askew and Dream Apart don't include certain mechanical things, such as being GMless, using tokens with weak/regular/strong moves, etc. Because of that, it would be very possible to make a "Belonging Outside Belonging" game that plays very differently from Dream Askew.
Of course, this is true of PBTA as well —Dream Askew itself is a PBTA game that plays a lot differently than Apocalypse World.
But because Vincent Baker hasn't defined (afaik) "PBTA" as anything other than games which take inspiration from AW and decide to use the label for themselves, thematic content is not necessarily one of the uniting threads between all PBTA games, therefore Dungeon World, which is PBTA, and mechanically functions a lot more like AW than Dream Askew does, is much more different thematically to Apocalypse World. Whereas, with Belonging Outside Belonging, it would be possible to make a game that plays very similarly to Dream Askew, and feels very similar mechanically, but which doesn't touch on any of these points. So my question is not so much "what exactly counts as Belonging Outside Belonging," but rather, is this choice to exclude most of Dream Askew's mechanics from the framework of Belonging Outside Belonging, as it has been outlined here, deliberate? And therefore, does that mean that there is theoretically a second lineage of Dream Askew hacks, one that is much more a lineage of "reskinning," for lack of a better word?