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It seems obvious to me that the story is dualist. It doesn't matter that it isn't scientifically serious (imo no theory of consciousness is scientifically serious, btw)
There are no decisions to be made, decisions don't exist in that way.
(I reread the story to make sure I was being fair. I stand by my point, but the story does execute on its (imo bad) premise well. I think over the years since I first read it I let that issue overshadow its good points -- it is an enjoyable and somewhat thoughtful work.)
I'm a Dennett fan, but I can agree it's a hard problem; the hard problem, even. But even so, there are answers which are clearly incorrect. I'd argue all forms of dualism fall into that category, but the story puts forward a particularly nonsensical variant in which there is a soul... but it doesn't do anything. It thinks it does -- the story talks a lot about putting on a performance of what the characters would have done if they couldn't perceive the future -- but it in fact does not, because every last atom in their bodies behaves identically to how it otherwise would. The soul has no causal or explanatory role on any observation except the subjective experience of perceiving the future. Why would it work like this? Obviously such a thing would never evolve -- it can't provide any fitness benefit since it doesn't do anything. Why would god or whoever make people this way? It's not like the soul is responsible for the body's actions: those were set in stone when the universe was created, and, anyway, that would require the soul to do something, which it never does.
I'm not opposed to speculative fiction exploring dualism, but Story of Your Life gets very into the weeds on physics and the determinism it builds up to is 100% grounded in physical laws... and then it abandons that premise to shoehorn in something nonphysical -- the soul -- but it can't actually let it affect anything or it would break the whole story. And note: the variational laws don't supersede the causal laws, they are equivalent to them. There's no trick here that lets you violate causality, and the future cannot cause the past.
... Except the heptapods actually do behave differently because of the way they perceive time! They don't write their sentences one character at a time but just efficiently use each stroke for several characters. And forget that: their very form or writing induces simultaneous consciousness! They (seem to be) confused by physical principles described from a linear time perspective! They're very patient for explorers (because, it's implied, they already have the answers they'll only actually learn later.) It's mentioned that our main character only imperfectly experiences simultaneous consciousness, but that should still only affect the subjective experience (as otherwise the future would affect the past, which remains impossible). And in fact she can't drop any hints about simultaneous consciousness, has to act exactly as though her subjective experience hadn't changed at all. Why the disconnect?
Determinism doesn't actually render the concept of a decision meaningless, it just means that decisions are part of the causal chain that will inevitably result in the future. While it is trivially true that "You will choose to do X because X is what you will choose to do," there must still be other reasons why you will choose to do X that make no reference to the future. My point is that the entire decision-making apparatus must still exist (or causality would be violated), so you're postulating an entire second self to make this work, and the self that perceives the future is extraneous.
Dualism is very sneaky. Like you said, it makes very little logical sense; it almost certainly doesn't describe anything real. But it's so hard to get over our instinctive belief in it. It can show up in many ways, some of them quite subtle.
My personal bugbear is the Doomsday Argument, which many rationalists believe, including Scott. But for a statistical argument like this one to work, there has to be some actual selection process, not metaphorical, not a clever turn of phrase, but a really truly actually real random lottery. And such a process requires the absurd form of dualism that you've mentioned. Your soul has to be presented with the deterministic universe as a whole, with all the humans that will ever live already set in stone, and will then "find itself" (the obscuring language Wikipedia uses) in one of the humans. And which one you inhabit can't have a physical effect on anything, because otherwise how could future humans have been available as a choice?
In an experiment where you create a simulated universe in your basement, flip a coin to determine whether it will simulate 2 entities or 20, and then ask entity #2 what it thinks the coin flip was, of course it should say 50/50. Repeating the experiment will show it's miscalibrated if it says anything else. Now, if duality holds, then perhaps some soul came along and is "surprised" to be inhabiting entity #2 in a universe that could have up to 20, and maybe that soul is subjectively correct to believe in the Doomsday Argument. But like the main character of Story of Your Life, that realization can't be shared with anyone else. When you ask the entity what it thinks, it can't give a different response based on whether this time it's souled or a p-zombie. So it has to give the averaged answer: 50/50.
Despite the resultant absurdity, the idea of "finding yourself" as a particular human - that your awareness is separable from the body you inhabit - still survives in a Wikipedia article. And in Scott's writings. It's embarrassing that rationalism isn't enough to conquer this trope.
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In a perfectly simulated universe, all decisions are predictable, including any decisions you make after learning the future and learning that you learned the future etc, recursively, forever, blah blah blah. This is not a narratively or philosophically interesting concept. Quantum mechanics aside, ultimate determinism and therefore hypothetical foresight given total information and a fully comprehensive universe model has been the default assumption among most smart people for a long time. Chiang does nothing in the story to say anything interesting about this at all.
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