Hmmm. Late answer, but I think it depends. Not even on what kind of rules or crunch is added, but how much and how many different kinds?
Looking at the Designing New Games section of the Dream Askew/Dream Apart book, it actually addresses this at the end. It even gives some suggestions on how to add in new elements, advising that you need to remember that any changes will ripple through the whole design and so need to be thought out carefully to figure out how to make them integrate smoothly. But then it notes:
"The other thing to keep in mind is that as your game drifts farther from the line established by Dream Askew and Dream Apart, it’ll also be drifting closer to the design space of other games. And that’s great! That means you have new resources to contemplate and borrow from. Look to other games for ideas about how to execute your goals."
Even this isn't saying it'll become not a Belonging Outside Belonging game or that you can't call it that. But it does have a good point that you drift further away from BoB, and it does start becoming a little less that and a little more something else. I don't think there's a solid line where it would stop "counting" or you'd be absolutely wrong to call it that. Belonging Outside Belonging is, as the book says, "about marginalized groups establishing an independent community, just outside the boundaries of a dominant culture... [that has] a hopeful, precarious, vulnerable quality to them." I'd say that if there's a core quality your game might have to have to be BoB, it'd really just need to have that "hopeful, precarious, vulnerable, independent group creating their own space and coming together outside of larger society" element to it. But even then I'd argue that if your game had literally every other element but was just about a club at a college and didn't really separate the characters out from the rest of the school or town, it'd still be fair to call it that, since it's so 100% the BoB system.
But I feel like if you adjust multiple elements, add multiple things and take away other things and otherwise tweak it to greater degrees, it becomes fair to call it more its own system inspired by BoB/with BoB elements. I think if you make a game with a GM, or add in dice rolls, or change/take out tokens, or take out playbooks and shift to a different character creation system, I honestly think any of those changes individually wouldn't make it not Belonging Outside Belonging. Even a couple of them wouldn't. But if you tweak it so that it's a game with a GM, you create characters without playbooks and roll dice, and there are no tokens, I think it's changed enough in mechanics that "inspired by" becomes fairer to say. Which is very cool, because then it's kinda evolved into your own game system.
Have you looked at Undying and Alone on Silver Wings? Both mark themselves as Powered by the Apocalypse and yet they challenged me to what might mean at first.
In this case I'm looking at 2 version, I have one that takes the tokens and makes them basically also count as "bestowed favor" on minions. That's my vampire game right now.
I also have one that gets very tactical for a single conflict then drops all the dice and stuff and goes back to the normal game unless there's another INTENSE moment like a combat or something.
I haven't looked into Alone on Silver Wings, but I've read through Undying and I'm a fan of quite a bit of what it does! It's neat, and kinda feels like someone took Urban Shadows and added even more World of Darkness flavor and elements into it. I think it definitely doesn't drift too far away from the core elements of what most people think of as Powered by the Apocalypse games, though, and while it adds things it doesn't take away much. There's a GM, there are basic moves, there are debts that tie characters together that they can use on one another, there are playbooks that all have playbook moves -- even the Status Moves and status feels a little like an alternative to Corruption. It definitely adds in some awesome new things, but I can see why it calls itself a PbtA, since it sticks very close to the recognizable framework as well.
(I also think this way about City of Mist, which takes out playbook moves entirely, takes out stats and changes how statuses work, and adds in the tags system, which I absolutely love, and has you build your own character out of choosing multiple playbooks and combining them, which is just a super neat concept to me. It's still got so much of the Powered by the Apocalypse that it's still very recognizable as such, imo, even despite the pretty extensive changes it makes! So this can also obviously be pretty subjective and depend entirely on the individual game and the person "judging" whether it fits the framework enough or not.)
As it is, I think both your game ideas still stay really close to the Belonging Outside Belonging framework! From what you're saying, one adds a slight change to what tokens can do by adding in one more thing they can do? And the other adds in dice only during certain moments but otherwise goes back to the "standard" BoB gameplay. Of course, you're talking specifically about working on these for the game jam and the guy running it talked about staying as close to the basic framework as possible (in which case I'd say your vampire one might indeed be more suitable for the jam), but that's more "what this specific jam is looking for" and less "what would be fair to still call Belonging Outside Belonging." The latter might be wider than the former for any given jam.
Heh you're right. What I ended up doing was making three games for it, 2 are already out. I decided I should try to please him first, then please this other person with the vampire game, then please myself for dice heavy. I wanted to honor the intent of the jam and the constraint. If I get the third one done, I'll put it out there too.
I really appreciate the feedback on the ideas/if it counts stuff. I was wrestling with it.
The reason I mentioned undying and alone on silver wings is because my first reaction was "hey that's not pbta" before I took a closer look.