The aliens did not evolve on the surface
These aliens evolved from ant/bug/worm-creatures, possibly moles if you want a more mammal origin. They never cared about how the surface looked, and only cared about 3D connectivity and branching. It's likely that they couldn't even see.
In the beginning their maps were made out of knotted straws, where knots indicates a larger hollow or other points of interest, and branching was made by tying another straw. This would be superficially similar to our quipu used for bookkeeping. 920
If the map had to be more accurate it had to be made out of something stiffer, like twigs or roots, so that directions such as up/west/east could be recorded.
Surface points would be marked in a way to show the type of environment around it: field, rocky, woods, close to water, etc.
The version made out of straw would be portable because you can just fold it down to a small ball, and keep the relevant sections unfolded. This would of course require training and maybe special equipment to keep it from tangling.
Move to the surface
When this race started caring about the surface of the whole planet, the maps would still be made in the same way as had been previously done: folded straw/twig sections, the more advanced the society got, the more advanced materials could be used, and portable maps would be intricate jointed constructions automatically folded by small machinery.
However, they had never needed anything flat to write on and it would never occur to them to ever make a 2D projection of something that was not 2D from the beginning - especially since they don't rely on vision.
Forced 2D projection
Even though you want a classical 2D projection, this would be unnatural for these guys and would probably only be constructed for trading purposes with other species. This map would only contain points-of-entry to the rest of the 3D network, and they would have no real concept of "projection", so the map would very likely be divided into sections sized so that the curvature would not cause too much of a distortion, and then these sections would be printed out next to each other. Think of hexagons or square tiles. The closest system I could find today is the "interrupted Goode homolosine projection":
It would probably not have any borders at all, just point clusters - the different nations would just be separate sections, with textual descriptions on how the pieces should fit together. 204