"Software" isn't the point. You can do the exact same math on CPU or GPU. OpenGL supports nearest neighbor texture filtering on whatever hardware you run it on since 1992, one year before Doom even came out.

But in practice, this didn't happen, which is what TFA seems to be all about. So it's not incorrect to talk about software renderers (of the time) vs hardware accelerated graphics (of the time) and how they were used in practice (at the time). It's just cumbersome to write "at the time", and it's understood from context; at least I did. It also helps to look at the rest of the blog's articles and what the blog is about...