But Lara doesn't develop as a character. I'm not sure quite what it is about this game that has fooled people into believing that it's award winning literature.
Lara isn't flawed to begin with. She's touted as being brilliant in her field of work, having an eye for new details and willing to take risks (go into the dragon's triangle.) A couple of people aren't on her side initially but that's them, not her. There is nothing about her to improve. That's a poor start when you're looking to develop a character.
Then she's thrown into a bad situation where she has to do or die. Putting aside the crazy stunts she performs (which mostly transcend human ability or limits of endurance) most people would rise to the occasion in her situation and be able to do what she does because their very survival is at stake. Sure, there are some comments about her parents and some hints that she can't live up to whatever legacy they have forged, but the details are far too sparse and it all feels so bare bones as to be non existent.
Lara "develops" in her situation as any human would. The OP is right, you could replace Lara with anyone else, any gender, and you'd get the same exact storyline. That's the problem right there, this isn't a personal story about Lara, it's just an old time clichéd survival story about some chick on an island. Lara hasn't been reinvented, she's been homogenised.