I think the terms here are doing all the heavy lifting.
What is shared imagination?
What is game play?
What is an RPG?
What is a board game?
Also how do you determine whether something is core or flavor-heavy?
Going a bit deeper, my initial analysis is that you are just making a circular claim -
‘An RPG is game that cannot be played without shared imagination’.
‘Shared Imagination is the core game play of an RPG’.
RPGs are characterised by paradigms. Of course a tradition can depart from paradigms over time; but RPGs have not yet done that very much. And as I've argued in this thread, classic D&D is certainly one of the paradigms.
I am asserting that one key thing that characterises these paradigms, and the games that resemble them - and that distinguishes them from games that are based around the production and analysis of complex patterns (eg chess, cards, other boardgames) - is that they involve the collective creation, maintenance and change of a shared imaginative situation.
This is not sufficient, of course, because it also characterises some storytelling games. RPGs also involve a distinctive way in which most participants engage with the fiction, namely, via the allocation of each participant to a particular character, whose actions they declare. But the shared imagination - which means that the only limit on a permissible game move is that everyone agrees it is something that can be done by that character in the fiction - is crucial.
The core of an RPG is a game about a fictional world where players control a fictional character where the players choices for the character drive the gameplay.
This makes Forbidden Island a RPG. Which it obviously is not.
Because the fiction doesn't matter to resolution: it doesn't create the space of permissible moves, nor does it factor into working out what happens when a move is made.
IMO, any game can be tokenized. Any tokenized game can be played solely in the abstract without tokens. And if this is accepted then being tokenized or abstract isn’t a core differentiator of any game type.
I already posted the example from Moldvay Basic, of one (tall) character taking another (short) character on his shoulders so that they could together cross the pool. I've mentioned sound being heard, and triggering responses, in 300'. Tapping things with 10' poles.
To this we could add moving the torch sconce, removing its screws or rivets, polishing it (like Aladdin and his lamp), perhaps with a linen cloth or a piece of leather or a square of silk.
Anything that I can imagine my character doing, given the situation they are in, is a permissible move in a RPG. These cannot all be tokenised (in advance), because my capacity to imagine the life of a human being in the sorts of situations involved in RPGs cannot be tokenised.
And that's before we get to consequences (eg if the GM calls for a check, and as a result the small NPC falls off the shoulders of the big one). She gets wet. She lands on some floating debris. Her leather shoes are ruined. Or not. These things can't be tokenised either, but they are all part of RPGing, and have been for over 40 years.