What about role-playing and character development? There’s not really much puzzle-y about your choices in The Baron. There’s certainly things you might miss, but the trick isn’t to think of something that works to produce an end game. Menu-based conversation is even more obviously not-a-puzzle, but still produces change.
What some people seem to be arguing is that story progression is always based on a puzzle, which just isn’t true. Some story progression feels more interactive than others, but I don’t think that interactivity relies on puzzles per se, but on feeling like your character has agency. I’ve had satisfying experiences with games that are just phenomenally juicy, and games that left it open to me to make up my own progressing story, and games that tried really hard to present open storylines. Alabaster has some puzzles, but you can play in a near-puzzleless state, following suggested cues, and still feel like you have an impact.
And what about games like Aisle, where you might never figure out all your options, but figuring out a sizeable number of them is trivial? The puzzle figuring out endings is entirely external to the story and player, not character dependent.
In general, I’d say story progression, even if it doesn’t depend on a puzzle, increases investment, especially when it appears to react in response to the character. I don’t think it needs to be puzzle-based. Poorly done, puzzleless story progression can feel like a cut scene or railed - think about games where you need to press “z” seven times in a row to get through dialogue - but that’s just a poor design choice. That same dialogue, with you “participating” can be engaging, even if the result is always the same, even if it’s always clear what to type.
Think about classic western RPG’s. Most of them have conversation options even when there’s no choices. The villain is always going to attack you in the end, but you often have different lines you can deliver. Often they’re variations on the same theme (“die, scum!”). Why do that? Well, because interaction, even trivial interaction, helps immersion, and well-written choices help role-playing. You feel like you have an impact in western RPGs because the story progresses in response to your actions, even if those actions are little bulletpoints in a journal.
As a player, some puzzles make me feel connected with the game/story/character, and some don’t. Being stuck hardly ever feels like an in-character thing - it is actively disengaging for me. Poorly designed puzzles can require external knowledge. “Thinking like the protagonist” is often way less helpful than I’d expect, and sometimes a really bad idea. (I love Lost Pig. A lot. But it requires you to be way smarter than Grunk could ever be on his best day.)
I’d say puzzles are one tool for connecting players with the game, but they’re a double-edged sword. Good writing, juice, story progression, offering clear choice that changes the world - these are other ways of making people feel invested and involved.
(Sorry if this was disjointed - I’m on some pretty heavy duty meds at the moment, and everything’s all foggy and vague.)