the 2000s have produced some of the best games of all time like the Souls series, Baldur's Gate 2 , Call of Duty 4, Splinter Cell and a few others... However, I feel the 90s was just iconic because so many new genres were created. Survival horror was created with Resident Evil... Yes you had Alone in the Dark, but the genre didn't really boom until Resident Evil. You also had RE's competion in Silent Hill.
You had the party brawler in Smash Brothers. Mario 64 was amazing for 3d platformers at the time. Rpgs in the 90s were unsurpassed. You had way too many classics like Final Fantasy Tactics, Alundra, FF6, FF7, Chrono Trigger, Suikoden I & II, Arc the Lad series, Lunar SSS and EB, Breath of Fire III, Shining Force, Xenogears, and countless others. You had amazing 2d platformers like Donkey Kong Country 1 - 3, Yoshi's Island, Sonic, Tomba, Megaman X etc.... amazing side scrollers like Shinobi 3. Historic games like Metal Gear Solid. Amazing smaller studio titles like Tenchu or Parappa the Rapper. Sidescrolling shooters like Contra 4 and Hard Corps, Metal Slug, among others. How about some of the definitive series in RTS games like Command and Conquer or Warcraft? How about the original X-Com? Fun party games like Poy Poy and Super Bomberman.
How many amazing fighters were being produced back then? You had Street Fighter 2 come in and basically become the definitive title for the 2d fighter genre. Then we also got SF Alpha series, Samurai Shodown, Xmen vs Street Fighter, Last Blade. Then we got some of the genre busting 3d titles like Tekken 2 and the Virtua Fighter series. The 90s were when the big 3 (Sony, Sega and Nintendo) were in their prime and actively battling it out.