I think that might be the "affine texture mapping". The original Playstation used affine texture mapping, which is known for causing distortion when the polygon is viewed at certain angles. The retro shaders by dsoft20 (which I used in this project) feature affine texture mapping to try and accurately recreate the look of old PS1 games.
Looking at dsoft20's github page again, there's a note towards the bottom warning that the effect is most noticeable on quads, and suggests adding triangles to the mesh to "avoid excessive distortion". I'll definitely have to keep that in mind in future when I attempt this kind of project again. ^^"