There's a nice example on that page with an overlayed relief shaded map and the original. Can you explain in English step by step how you would turn one into the other manually using something like photoshop?
Use the partial derivatives of the topo height to calculate a normal. dot that normal against your fake sun angle to shade your terrain.
it seems though that the magic in this is in throwing away specific details and changing the sun angle when it is aesthetically pleasing which makes sense.
on the surface it looks like you should be able to use the heightfield and standard filters to get a reasonable result but I'll take their word for it that real world data will prove more difficult.
If you read the text of the site or the paper: it needs a digital elevation model (i.e. a height map) to create the shaded relief. It does not ingest graphical maps and does the relief, it needs a discretized map of height data, such as lidar (which can be downloaded for any place on earth with 1m resolution).