Hm... at first blush, I have to agree with Swiss.
Maybe it's a trick of the camera and lighting, but I don't think linen would be so reflective and the weave looks too wide (open), though it's difficult to get a sense of scale from the picture- the reflectivity *might* be due to the adhesive used rather than from the "linen" itself, but that is a total guess.
In the picture it almost looks like plasterer's (acrylic or nylon?) reinforcing weave which has been stretched here and there to create irregularities in the weave.
Disclaimer: I am absolutely NOT an expert. But I do own some heirloom linen items (bed sheets and French wedding stationary dating from the '30s with a decorative backing in what I believe to be linen). The linen on the wedding reception cards (which is closer to the same use as a map) was of a decorative design and does not exhibit any glossiness. As some ends of the design have come loose and there is no glossiness at all (indeed, it's difficult to tell what adhesive was used) I think it's most likely an ordinary water soluble white glue was used sparingly to lightly tack the design to the card- though I'm not sure of this as the moisture of white glue would probably affect the underlying cardboard and there's no sign of that having occurred. I'd ask my grandmother (it was for her wedding) but that would involve the use of a Ouija board
Anyway, my first gut reaction to Swiss' comment was "hmmm... that DOES look fishy".
I dunno... just throwing some thoughts out there.