It looks to me like the original gradient based shading code is just wrong. Maybe there are numerical problems due to its frivolous use of trig functions, or more likely the way it calculates gradients is just broken. But shading based on slope should obviously make all zero slope areas (like water) the same color, and the fact that it doesn't means it isn't working.

The raycasting code in this article, on the other hand, seems to be missing the Lambert term! Just because a surface is not in shadow doesn't mean that it will appear at uniform brightness. If it is diffuse/matte, which seems like a reasonable starting point for most terrain, each light ray L should have a contribution to the brightness of the point proportional to L dot N, where N is the normal vector of the surface (and to find that you need, sorry, the gradient). In short, light almost tangent to the surface doesn't illuminate it much. Other kinds of surfaces will have different BRDFs (e.g. they can be shiny) but none of them will have the completely unshaded behavior shown. Of course, it's fine to do totally nonphysical things if it helps emphasize some aspect of the data, but it doesn't seem to be done knowingly and I think it produces a misleadingly flat look.