Why is the Nikkor 35mm f/1.4 way, way bigger than the Nikkor 35mm f/1.8 (DX)?

Like, is the 1.4 hole way, way bigger than the 1.8 hole that you need to have a larger lens construction? Or is it because it works on FX with a different sensor?

More of a technical question on schematics than for general-use photography.

Yes to both

FX lenses are bigger because they need to cover a larger area. Fast lenses also increase size, since the diaphragm has to be larger as well.

Part of it is that, as expected by definition, an f1.4 lens of a given focal length has a larger diameter than an f1.8. However, adding to the weight and bulk is the complication of trying to get the aberrations corrected for a flat field that covers the wider sensor, and the even more complication of trying to correct the aberrations for the wider aperture. It's just not as easy as scaling things up.

It is primarily because the 35mm f/1.4 is a wide angle full-frame lens whereas the f/1.8 is a normal DX lens.

Look at the Nikkor 50mm f/1.8 D and the 50mm f/1.4 D. Both are full-frame normal lenses and they are nearly identical in size.