Note: I don't ask here why did they created "maps of worlds" at all. That has been mainly answered in this question.
My question is: why map exactly, as a way of (visually) forming "maps of worlds"? What is the point of this? Why not use for example a random land distribution for each world?
I could understand if they used the map of their home world (they done this btw). But what is the point of using the map accurately reproducing land structure of a strange world? (I assume accuracy because Louis Wu recognized the map of Earth)
Who could need that? Strange world natives? Obviously no. Land outline is probably the least significant feature defining the conditions of particular location. At least the natives shouldn't care about it (if they had idea about it at all). Looking up is enough to have convinced they're not home. This feature cannot even help reproduce population distribution of a strange world since the Engineers haven't collected whole population from each strange world.
Did the Ringworld Engineers really need that? I really doubt. I don't see any plausible reason why such advanced civilization as the Engineers could use such imperfect thing as map projection. Whichever kind of projection you use, something always get distorted. Furthermore such processes as continental drift can drastically change appearance of planet surface in a few million years. So, for example, if map of Earth would have been formed on Ringworld ten millions years ago (using contemporary Earth as a sample), then likely Louis Wu couldn't recognized it.
AFAIR the shadow squares had surveillance equipment which allowed to watch the Ringworld surface in detail. Suppose the surveillance staff (people or computers, no matter) need identify an observable area or find certain location. Is visual comparison of land outlines a convenient way to identify area location? I think the Engineers race could definitely come up with something better (a GPS-like system, for example).
So why flatten map?