Most of the "3D" we see is made up by our brains. For evidence of this, look at a photograph, and look at how far away things are.

Having eyes spaced apart does help us to tell the distance to things that are close to us, but that is only useful for a short distance. Our brains also track the parallax and occlusion of numerous objects, which helps over longer distances, but works just fine with 1 eye.

I think there are two ways eyes could work in higher spacial dimensions, you could either have an n dimensional eye, which percieves an n-1 dimensional image, and then an understanding of "distance" is used to fill in the remaining information, or (which may just be my own 3D-ness showing) you could have several 3D eyes in different directions, each percieving different 2D images, with enough overlap to fully see the n-dimensional space. That would take n-1 eyes to properly see.