No, it's due to limited precision in the vertices. If you had 64 bit integers you could have 32.32 fixed-point and it would look as good as floating-point.

did you watch the video?

Quake did not use floating point in it's rasterization math, and it exhibited none of the jittery polygon issues that the ps1 did. It's largely a lack of subpixel accurate rasterization causing it (not even sure if PS1 is pixel accurate, let alone subpixel :)) .

MVG isn't exactly an expert on 3D graphics.

Quake had perspective correct texture mapping though, something that the PSX didn't have.

Sure, but lack of perspective correct texturing is a separate issue, with a separate visual artifact.

Jittery polygons refers to the artifacts you get when polygon vertices are snapped to integer pixel coordinates, rather than taking into account subpixel positions. Quake did not have this issue, despite not using floating-point calculation in it's rasterization. It did use floating point when texturing spans, after rasterization, but this was more of an optimization than a fundamental requirement for accurate texturing :)