I'd say it's got nothing to do with the games, and everything to do with us as long time gamers. I used to get terrified of death and losing on things like Tomb Raider II and III, spent hours doing etc etc what you said about nightfire.
I replayed the two games recently, and none of that emotion was there. The games were the same, the characters identical, but I've been gaming for over a decade now, they just don't affect me the same.
That said,this is more of my issue, as previously stated. If a storyline is good, then a character death in-story will still affect me just as much, sometimes more, than in the old days. I think nowadays I pay more attention to the characters than to the magic of controlling a nubile young archaeologist, and it makes the whole experience much more enjoyable.