So the past few years when I think PS1 games like Metal Gear Solid, Resident Evil, Parasite Eve and Final Fantasy VII I have this weird feeling of emotional attachment, I can't even explain, but it's a weird feeling.

It's called nostalgia.

It's nostalgia. I feel the same way about early ps2 games like Jak, Ratchet and Clank, and Sly Cooper

But I only started playing those games in 2015.

That's still enough time for you to become nostalgic.

when you truly enjoy something, youre more open to it being a part of your life. having it starts to feel so natural that being without it almost feels crippling (cell phones are a great modern example). you dont just think of it as a thing anymore, but rather a part of yourself

I have a few that I don't think nostalgia covers. That's because these games were special from the start.

Final Fantasy VI - I had effectively quit gaming when I found a used copy while with a friend. I remember that I enjoyed FF1 years before so I bought it on a whim. It was a revelation. It was what I had wanted all along from gaming without knowing it. It didn't get me totally back into gaming (because I couldn't find anything else like it) but it did make me pay attention to where gaming was going and set the stage for me buying a PS1.

Suikoden - Again, I bought this on a whim for like $5 used at a video store. I'd never heard of it before. However, I can still clearly remember the moment when I first started it up. It another, "THIS WHAT I'VE BEEN LOOKING FOR," kind of thing.

Final Fantasy Tactics - My gaming Spirit Animal. I leveled up perfect saves like three or four times. If gameplay was ever designed just for me, it would be this.

ICO - This was a big one. I remember how I felt during the bridge scene like it was yesterday. I just sat there in shock. Same thing with the ending. That game grabbed me like no other game ever had before. It made me realize that gaming had an insane amount of potential beyond the norm. It was also the first game to wrap me up so tightly that I felt true and honest anger toward the antagonist.

Valkyria Chronicles - Let's just say that it hit me hard. I cried. Not only did I stop playing for several days, I didn't even want to look at my PS3. I hid the game case so I wouldn't see it. I kind of hate that I love the game so much because I can still taste the bitterness.

It's not an attachment to the game. It's an attachment to the time when you played them.

Its definitely nostalgia. The feeling is even stronger the more atmospheric the game is.

I understand you, because i feel the same. great titles with emotional attachment. If you are looking for games with strong emotions / attachment and an incredible story:

Metal Gear Solid 1-4 :)

Persona 3, 4 and 5 :)

Maybe the Yakuza-Games (all will be available on PS4, Yakuza Zero is a good start for newcomer)

These games have a strong bond with the player. The reasons: Many interesting / unique characters, extremely sad deaths/emotions and strong twists. In the Metal Gear Solid (1-4) Games I also found the philosophy and psychology awesome. There are other great games with a strong bond too, like (for example) "The Last of Us" - but the other games can give you the special feeling of what triggered FFVII, MGS1 ect. :)