I can try. I was obsessed with this game when it was new, but I was young (12 to 14 years old) and not nearly as analytical and experienced in software as I am now, so going back a lot with memory.
The world the game created felt so much more real than any other FPS at the time. The 3D graphics (true 3D was new at the time) were absolutely stunning. The N64 controls were also very novel and incredible, which added significantly to the feel. The trigger button, the rumble pack, the joystickj, etc were very new.
The different weapons available were varied by capabilities and limitations, and led to some fun and interesting scenarios and strategies. They had a perfect selection of weapons from pistols to assault rifles (I think that was the name), and the single player used the weapons perfectly in line with the scenarios, while the multiplayers sprinkled them in interesting combinations around the level for you to find.
The objectives were complex enough that they weren't a given and required some thought and strategy, particularly on 00 agent mode (the hardest mode). The whole game told a cohesive (and interesting) story, much like an interactive movie. The objectives also varied based on difficulty setting. Some were as simple as "walk into room X" and others were more complex like "Place a C4 charge on each terminal in the entire level."
The difficulty changes also extended gameplay and replayability by miles. A novice could easily beat some of the early levels on the easiest setting, so the game wasn't too hard to scare away new players, but the difficulty/complexity scaled up so that even expert players had a hard time beating the upper levels on hard setting.
Lastly the multiplayer was incredible and fairly novel. The N64 allowed 4 players and the levels were interesteing. Complex enough that it allowed for the development of solid strategy, but simple enough that you could pick it up fairly new and be able to get the hang of it.
Actually lastly, the game was one of the first FPS that was mainstream, so nearly everbyody knew somebody else who had the game or wanted to play. We would have Goldeneye Parties where we'd take turns on missions, or do multiplayer, etc. It was an absolute blast.
P.S. Now in my late 30s, my brother (who still has an N64) often brings Goldeneye to family reunions and we play and reminisce about the good old days. Definitely a very impactful game for us.