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