I’m not, on a structural level, in love with choice games with psychologically well defined protagonists. It strikes me as conceptually backwards: if you’re telling me who the character is, why are you then asking me what the character does? Shouldn’t the latter flow directly from the former? Although it probably wouldn’t be workable on a large scale, I’d be interested in a game that just quizzed me on my characters feelings, opinions, and personality, and then set that character loose to make their own decisions without my further input.
That having been said, I think people tend not to notice or be bothered by railroads if said railroads are taking them where they want to go. If you describe an emotional reaction, and that reaction makes sense for how the player imagines the character, and they’re imagining a character they find interesting and/or sympathetic, they’re not going to notice that they weren’t directly consulted. The choice being made for them is the choice they would have made anyway.
Therefore, my conceptual objections aside, the practical question is less about whether or not you define the character, and more about how you define the character. If you know in broad terms who your target audience is and what’s likely to resonate with them, you’ll have a lot more leeway to make assumptions for the PC.
Think about the story you want to tell, what minimum assumptions you have to make about the PC for that story to work in terms of plot and theme, and look for emotional reactions that feel inevitable for any version of that character. There will probably be enough of them to keep the story from feeling bland and robotic.
Then, if a player objects to being assigned a given emotion, try to determine why it rings false. If the player wants to portray a character that isn’t compatible with your core assumption, then see previous comments about not being able to please everyone and move on.
On the other hand, you might be inadvertently assigning the character traits that don’t flow from, or are even incompatible with that core character.
The biggest concern here is that you might be assuming reactions you haven’t earned. Even in a static, 3rd person story, the emotional reactions of the character obviously still need to be justified by what’s going on. If you announce that “Bob was frightened” and nothing especially frightening is going on, then readers are going to assume Bob is neurotic or a coward, whether or not that’s the author’s intention. If Bob is the character the player is being asked to assume the identity of, that disconnect is going to be even worse .