There were some truly amazing games that year.
Metal Gear Solid 2 was really my favorite of the bunch as it delivered a high level of detail at 60 fps with so many incredible effects that we had never before seen.
GT3 came out running at 60 fps as well with highly detailed models, brilliant reflections, and even doing things like simulating the effect of sunlight on the road.
Silent Hill 2 was released in September of that year and was the very first game to feature fully dynamic soft shadows cast by a light source. All objects in the world could cast proper, soft shadows by pointing the flashlight at them. The game also featured high poly characters (for its day) on top of this.
ICO wasn't a technical showpiece, I suppose, but it DID deliver lighting effects the likes of which we had never really seen. The way the sunlight worked in that game was truly remarkable for 2001.
Halo didn't throw around all that much geometry for its time but it was one of the first examples of heavy pixel shader usage.
DOA3 featured obscenely detailed models and backgrounds running at 60 fps.
Rogue Squadron 2 offered some of the most detailed geometry ever seen in a game up to that point along with plenty of other effects (including full self-shadowing).
...and so it went on and on.
In 2001, the most demanding PC game was likely Max Payne. It looked nice enough, but environments and character models were extremely boxy, post processing was nowhere to be seen, and none of the modern shader effects made it in. It was an interesting time...