I had a look at some Quake 2 footage to be sure that was the version I remember playing on the original PlayStation back in the late 90s. It wasn't Quake 3 Arena or the original Quake so I reckon it must've been that one but I don't remember the graphics looking so abysmal.
Yeah, provided it's the right Quake 2, then I did complete it though the last boss battle was hard I recall. I loved the way the controller would violently rumble in your hand when some of the huge cyborg guys would come thumping past. That used to scare me silly as they had rockets and could wipe you out easy. I mastered my fear in the end though and made easy meat of them later on in the game.
I think Quake 2 was the one where you went through this prison cell block and you'd hear people crying "Help help let me out!" That always made me laugh. No, I'm not a sadist, it was just the funny slooow voice used. My little sister and I used to play the game sharing the same controller - I think I did the movement and she the shooting!