If you’ve ever sampled a texture in a shader, then you know what those are, so it’s probably fair to include them in the prerequisites for the article. But yes, those are intended to be approximate screen-space derivatives of whatever quantity you plug into them, and (I believe) on basically any hardware the approximation in question is a single-sided first difference, because the particular fragment (single-pixel contribution) you’re computing always exists in a 2×2 group of screen-space neighbours executing in lockstep.