In your example, as I understand it, Pia is doing some things - preparing and eating food, swimming in an ocean, sailing a vessel, etc - with things that Jo created or place in Pia's path.
So the analogue in RPGing would be a player picking up the GM's notes, reading them, folding some into paper hats, using others to light a fire, etc?
Or did you intend that Jo tells Pia to imagine doing all those things, and then to ask Jo what happens in the imagined circumstances?
That is the right question to ask. Were this occurring in the real world, then it can hardly be disputed that each possible Pia can tell their own story. However, in the game world what happens relies on a shared set of norms; existing in virtue of a common experience of life and of rules agreed between Jo and Pia that will say what is normal. (I'll cover ground here that I'm certain you're aware of, but hopefully serves a purpose in revealing thought processes.)
Thus, if what Jo means by "chair" is something that Pia also understands by "chair", the imagined upending of imaginary chairs goes as described. It is only in view of possible differences in what is meant by "chair" (Jo - "that is a
heavy chair, far too heavy for you to upend") that it becomes possible to talk in terms of Jo dictating Pia's acts, and then only to the extent of those differences.
The fictional positioning is therefore expected to be at times incomplete or in contradiction: Jo says "chair" meaning "heavy chair", while Pia hears "chair" thinking "wooden chair, one that I can upend." Just so long as Jo and Pia have a common experience of life or rules agreed then - so far as those extend - it can't really be disputed that each Pia can tell their own story. (Unless of course for every element described there is uniquely one future state: chairs
cannot be upended, chess games can only proceed along one line of play, water can only be swum in at the prescribed hour and place)!
A thought-experiment that segues into is the following...
Jo and Pia have between them a black-box. Where they have an agreed rule in force, that prevails. Lacking such a rule, when they have a life experience in common - such as chess positions and legal moves, or the recipe for a
bloody mary - that prevails. But whenever they imagine something that no life experience in common nor agreed rule provides a norm for, they each input what they want to become the norm to that black-box, which outputs the norm that they must go on with. The workings of the box are inscrutable.
It might be that the box contains an entity that deliberates and chooses, or perhaps Jo exercises mental control over its workings, or there are myriad algorithms chosen among according to some principles, or it could be using a weighted but randomised distribution. Or something else. On the subject of upendable chairs, then, Pia and Jo input their expected norms - U and non-U - to the box, and it ouputs U. Can Pia then claim free will? And what is the sort of free will that Pia can lay claim to?
A question I have in mind is, do two different Pias (two people working through these two thought experiments) feel bound to tell the same story? How widely can they picture their stories diverging?
And do the workings of the box matter to this? Suppose that the workings certainly had nothing to do with Jo, but came out only 10% of the time in Pia's favour. Is Pia freer to tell their own story then they would be if the box's outputs were 50% in their favour... but with Jo secretly controlling its functioning!?