This is tough year to vote, no matter how I look at it.
My favourite game from that year, by far, is Gothic. You know that 3rd person perspective, open world narrative RPG most people keep hearing about, that influenced so many developers (including Witcher devs), draws its influence from later "world simulation" Ultimas and has cult following, especially in Europe, yet not many people actually played it. Yeah, that one.
There was Arcanum: Of Steamworks and Magick Obscura. From the devs that created Fallout, but this time with a world that's even more reactive to you. I really liked it, but Steampunk is not my thing, so while mechanically better game than Fallout 1/2, it never rise to that status for me as FOs did.
Then there's Max Payne. Oh man, what a great action-adventure game with story and atmosphere soaking in noir genre, that introduced bullet time as a major gameplay concept.
But this is the year that has GTA III and Halo: CE. And while I don't generally like to vote for games that are sequels or refinements of previous ideas, these two were massive.
Eventually, I have to go with GTA III over Halo: CE, since FPS genre was not only well established, but had Half-Life happen just 2 years before that single-handedly changed (for better or worse) how FPS games were made from that point.
Other games I really liked form that year are Conker's Bad Fur Day, ICO, Return to Castle Wolfenstein, Black and White, Wizardry 8 and special mention goes to Severance: Blade of Darkness - Souls before Souls of a sorts, since it didn't have respawn mechanism, but overall gameplay and level design reminds of Souls, just with much more satisfying combat.