There's a specific chapter to look at in Dream Askew/Dream Apart that talks about this. The threads are important and part of the design ethos as much as the concept of like principles are to a pbta game. It might be a Belonging game but it would stray much further from Avery's original concept.
One example in the text is that without lures to encourage player interaction, that might result in more separation among the players and even a larp that had lures but made them more difficult to do might result in something moving towards the edge of the framework.
I suspect a good way to look at it is less as a binary and more as a spectrum where the elements might gradually shift it further afield from what the system was originally designed to express. The book itself is also highly recommended and is, in my opinion, one of the clearest pieces from a technical writing/teaching perspective and does a great job getting at the essence of what the system is and what it brings to the table.
I think it wouldn't be inappropriate it just might be Belonging inspired instead of an actual belonging game. Avery actually talks about this in a chapter about designing your own belonging game int he core book. If you go over to the belonging jam, you there are some resources you might find helpful.