The reason software rendering look different from 3D accelerated games (incl. 3Dfx) is nearest neighbor filtering and low resolution, which were necessary to keep a reasonable framerate. At the time, it was considered ugly, so if your hardware supported bilinear filtering for free, it was turned on, but it didn't have to.
In the time of fixed pipelines (3Dfx to GeForce 3), you couldn't do arbitrary operations on pixels, so some effects, like the kind that are common in the demoscene were software only. So games that used these effects, like Comanche voxels can indeed be thought as representative of software rendering, and they can, of course, be simulated on modern GPUs as everything that was done on software before can.
But the article uses Quake as an example. I may be wrong, but I don't think it does anything that can't be done by a fixed pipeline GPU. In fact, even keeping the same style (nearest neighbor filtering + low resolution), hardware rendering will probably look better because the GPU does proper perspective correction on every pixel. The tricks used by the Quake engine are awesome, but they don't beat raw power.