2001 was a year of smaller titles for me.
Actually, I never even played any of the main poll games. Not even Smash Melee (did play the original, Brawl and Ultimate though but that's besides the point), GTAIII (but did play the original, 2 and 4) or Halo (which my stepfather played a tiny but didn't like). This is mainly because our family never got a PS2. We already had a Dreamcast, two in fact, and because it looked at least as good graphically it made the PS2 seem unnecessary. By this year and the time Dreamcast died the beter looking GameCube and XBox came out so why would you still get something that's older and looks worse? Yes, our line of reasoning had some holes back in the day.
Meanwhile however the PC would get more and more of my playtime.
Even of the 'Others' list, I've only played Crash Bandicoot: The Wrath of Cortex (not "the Codex" ), Luigi's Mansion and Mario Kart Super Circuit. The fourth Crash game, which I played on GameCube, was actually quite good. It's sad that when the newer one came out they called it '4', disrespecting Wrath of Cortex. Luigi's Mansion was great though, I was quite surprised by this and it gave Luigi a unique identity which he still has today. The game has a fun story with a fun premise and fun enemies and fights. It was adventurous and memorable, and challenging enough with plenty to discover and uncover. It was a much better game than the GameCube's main Mario game, or even its Zelda game for that matter. Mario Kart Super Circuit though, the series first handheld entry, always disappointed me a bit.
However, regardless of this mild list, 2001 is still within the, though now declining, Golden Age, because it doesn't stop here. Even still in the console space, this year was also the year of the Zelda combo, Oracle of Seasons and Oracle of Ages on the GameBoy, though I wouldn't play those until years later when I went out of my way to track down full original copies of the Zelda games I missed when I was younger. The GameCube also saw some more playtime with Star Wars Rogue Squadron II. On PC though, I got to play some of Red Faction, and the rts Cossacks: European Wars. This game could have up to 8000 units all at once in a game. I remember me and my friend creating near 4000 strong armies of riflemen each, and then fire upon them with one cannon which would kill over a hundred units in a single shot, flinging them backwards. It was beyond epic. I also played quite a bit of the rts Empire Earth. This game starts you off in the stone age, and advances you all the way to the future. We came to realise, that once you get to the modern age, post World War II tech, you can just nuke everything all the time. Which was fun.
However the biggest impact would be Star Wars Galactic Battlegrounds. This rts, I had a bit of an rts streak, is built upon Age of Empires II, and it shows. It's almost no more than a sprite-swap, but that was okay when the foundation is this good. This would become one of my most played games of all-time, and we (the same friend) would play this for literally decades to come. We'd do multiplayer, always as a team against two or three hard AI. In fact, we played this just this last weekend. Even though you're playing AI, a match is quite difficult on the higher difficulty levels, because obviously, the AI cheats immensely.
Still, as a game, I think the game of all these that stuck with me most as a quality video game for this year was Luigi's Mansion. So my vote goes to "Other", for Luigi's Mansion.