No, LCDs are not crisp squares. Pretty much every screen type is still RGB in some kind of array. RGB stripe or Pentile are most common. You can also think about things like VR or a projector where your screen in transformed through a lens.
Everyone has to constantly compensate for this fundamental thing in computer graphics to this day.
Edit: As other things come to mind with how relevant this paper still is...
>antialiasing techniques, and image resampling seems to "mostly" assume that pixels do represent the average color over a square rather than a point sample. Not perfectly, but as a reasonable first-order approximation.
Not in the least. For example in texturing (wrapping images onto meshes), mip maps and bi/triliner filtering are very common. Assuming average color leads to a jagged (if you mean avg over one pixel) or blobby (if you mean average over several) mess. Mip maps are essentially point samples of a texture taken at different sample resolutions that are then resampled at runtime to form the best approximation. Essentially no one uses "average color."