Although I love primitive 3D tech, GBA and Playstation (and sometimes DS) have this "disgusting" effect when there is camera movement. I don´t know the term for it. Never seen it on N64 though.
tl;dr: It's probably the fact that there is no "antialiasing", and the screens are also too low-resolution on top of that, meaning all scaling effects (including the DS 3D unit) will look total garbage, no matter what.
I don't think there is an actual term name for it though.
Can't speak of the PS1, but pretty sure on the DS the vertex data is integers (that is, you can't have a vertex on a subpixel, so polygon movement will always look garbage), and on the GBA you have a whole other set of problems, but it also boils down to the lack of antialiasing on a low resolution display.
Although on the GBA, the ARM7 lacks a VPU (floating point processing unit, basically), meaning that you either emulate it in software (omegaslow), or you do it in fixed point (muuuuch faster, but loses precision no matter what).
Just by looking at the video linked a few posts before, they are undoubtedly using "mode7" graphics (which actually looks to be mode2 with an impossible 3rd layer for the HUD, but they are probably just using sprites for that instead), which means using affine transform (I won't detail that in this thread, sorry!), but it should have enough fixed point resolution to not look total garbage, so the problem in this case is definitely down to the low-resolution screen with a lack of antialiasing.