I've heard that game is really, really good but I've also heard it's only great if you're nostalgic for the sorts of things that are in the game, from what I'm told it's very early 90's~
Do you think I'd be able to enjoy it even though I was born in 1995 and won't get the majority of the references scattered around the house?
I'd say thats part of the appeal but in no way the main appeal.
Whether or not you would enjoy the game has to do with if you are okay with no traditional gameplay at all. Nothing. No puzzles...no nada. A non traditional narrative as well. Its basically a walking and letter reading simulator with occasional voice diaries. You piece the general story and the lives of these characters together with scraps basically.
Incredibly affecting for me, but I understand if some people aren't looking for this type of game/experience/whatever.
Edit: Again, the 90's vibe is amazing but in no way the "big deal" with this game. Great setting though. I got some of that nostalgia, but it also brings up memories of childhood and school and my parents and my brother and sister and my friends....etc.