The thing is, while the game attempts to say a lot about Lara by her circumstances and the things around her, all of that is being constantly refuted by the way Lara acts in person. Yeah, she's technically going on adventures of her own free will, but she herself doesn't seem to think so, mouthing off constantly about how this is something she's 'GOT to DO'. That's the classic cheap-ass writer trick for avoiding having to think of proper logic or motivation.
As an INTP myself, I can sympathize with the super-logical person that Yahtzee seems to be...to a point.
However, saying, "I've got to do this," "I need to know," or "I don't have a choice," when those statements are logically wrong when taken literally is not a "cheap writer trick for avoiding having to think of proper logic or motivation." What it is a situation where a person is compelled by an emotion or belief so strong that it FEELS impossible to ignore, even if it technically and logically is possible to ignore it.
For example, if my kids were the captives in Far Cry 3, and I was Jason Brody in Far Cry 3, and I had to do what Jason Brody does in Far Cry 3 to save them. If you asked me, "Why are you doing all this?" I would likely reply, "Because I have to. I have to save my children." Now, do I literally HAVE TO? No. In a literal sense, I'm choosing to do all that because I love my kids and I am choosing to go Far Cry on the human trafficking pirates. But that's not how I would feel in that situation, and expressing it that way would devalue my reality: I love my kids more than life, and I am compelled by that love and by duty as a parent to save and protect them. To say "Because I choose to" may be more logically accurate, but phrasing it that way would devalue that emotion. Me saying, "Because I have to" is characterizing my parental love and duty that compels me to (choose to) save them.
As literary example, Beowulf goes off to fight the dragon in his old age to protect his people because, in his mind, "I have to. If I don't do it, no one else will." This is logically wrong. He is choosing to. He also fails to recognize that the young, strong, and brave Wiglaf has the potential to carry his heroic mantle. But he goes off anyway, compelled by love for his people, his sense of duty to protect them, and his desire to uphold his heroic honor. Then he dies. Is that a "cheap writer trick for avoiding having to think of proper logic or motivation"? No! It's the ENTIRE POINT OF THAT STORY. Beowulf is the archetypal Anglo-Saxon hero, and the poem is an epic tragedy. Beowulf's "I have to do this" is characterizing him in VOLUMES: his honor, his loyalty, his pride, his strength (though it is waning), all of it. Is Beowulf poorly written? You could say no, but, well, you'd be wrong.
The point is, a character saying "I have to do this," though that might not be logically or literally true, is a characterization technique. It is a roundabout way of saying, "my sense of curiosity/honor/duty/loyalty/love is so strong that I feel helpless to resist, and I'm not going to, because my desire to follow it outweighs anything else to the point that I feel as though I have no choice in the matter."
I haven't played the game, so maybe the writing just doesn't sell the above idea. That's certainly possible. Or maybe Yahtzee is just an super "enlightened" bloke who doesn't let curiosity/honor/duty/loyalty/love ever stand in the way of logic, but that doesn't make those who do incomprehensible or poorly characterized people, it just makes them people he can't relate to.