It’s very useful to point out that it’s a Box Filter because the article moves on to using other filters, and larger clipping regions than a single pixel. This is framing the operation in known signal processing terminology, because that’s what you need to do in order to fully understand very high quality rendering.

Dig a little further into the “bilinear filter” and “bicubic filter” that follow the box filter discussion. They are more interesting than the box filter because the contribution of a clipped polygon is not constant across the polygon fragment, unlike the box filter which is constant across each fragment. Integrating non-constant contribution is where Green’s Theorem comes in.

It’s also conceptually useful to understand the equivalence between box filtering with analytic computation and box filtering with multi-sample point sampling. It is the same mathematical convolution in both cases, but it expressed very very differently depending on how you sample & integrate.