This is incorrect. It is exactly the same algorithm as circuits in the GPU or as instructions on the CPU. No difference, except one: the way data is pipelined on the GPU makes texture blending free, or nearly so. So to show off, every 3D game back then turned it on (an OpenGL/Glide/D3D configuration option) and everything got smoothed out, often with no option to turn it off. That's why it ends up looking different: because the game itself selected different interpolation in accelerated vs software rendered. It was a game choice.
These days you can use different presets to override those choices, and have your 8K, 240Hz Quake look software rasterized, if you want.
These days you can use different presets to override those choices, and have your 8K, 240Hz Quake look software rasterized, if you want.