I almost voted for GTA III considering its impact and how much I still like it (flaws and all) but I gotta vote with my heart with "Other" since my game for 2001 is Civilization III.
Back in the day, I started up my gaming life as a console gamer but due to some money-related issues I spent the last years of my childhood and early adolescence on PC. Out of many games I loved during those years, none have become so permanent in my life as Civ III has. For me, it's the ultimate strategy game. I tried Civ 4 but it just never clicked with me. I still have long Civ III playthroughs to this day. It's also perfect if you want a long game to keep you busy while listening to an audiobook which is pretty nice lol