There seems to be a problem with the gog version of this game that breaks the map screen - everything is way too dark except for a beam of light going across the screen diagonally. I found a solution to the problem.
First, create a new folder on your hard drive. Call it "giantsbak" or whatever.
Next, go to the folder where you installed the game. Move EVERYTHING from this folder to "giantsbak".
Download the Version 1.4 patch from this link:
http://giantswd.org/?file=2
Install it. Ignore any errors. It will automatically copy a number of files to the place where it thinks Giants is installed.
Go to back to the folder where you installed the game and then moved everything out of. You should see a few new files. One of them is called "gg_dx7r.dll". Move this file to "giantsbak," overwriting the newer and bigger one there, and delete everything else.
Finally, move everything from "giantsbak" back to the installation directory, and play the game.

Out of curiosity, could you (or anyone else) upload the GoG version of gg_dx7r.dll?
I showed this thread to Tasiin (the fellow that made GiantsHook and GRM), and he was interested in seeing what was causing the issue you were having.

The form only lets me upload images.
It's the same size as the file "gg_dx8r.dll" that comes with GiantsHook. A diff shows that the two files are mostly but not completely similar. I've also noticed that I have this problem if I install GiantsHook to a retail installation dir (which works fine on its own).

Could you try emailing it to z0pharx@gmail.com?
It sounds like they're using a modified version of the DirectX8 renderer that shipped with the GF3 version of Giants, so it'd be very interesting to take a look at what exactly they've changed in the new version.
Also, regarding GiantsHook - have you tried installing it without enabling the DirectX8 renderer option in the installer? Doing so should avoid any such problems, as it won't make any changes to which renderer that Giants uses.

Sent through Yousendit.
I tried installing GiantsHook to my "fixed" GoG installation but without the dx8 rendered. The map works fine, but I'm not noticing anything different in the game itself. I did patch the game through "GiantsHook Setup.exe".

Thanks! Got the file, sent it over to Tasiin so he can take a look at it.
And yeah, a lot of the graphical changes made by GiantsHook require the DX8 renderer, so you may end up having to choose between having them, or having a proper map screen.
At any rate, it'll be interesting to see what Tas turns up with his analysis of the DLL.

Please let us know if you hear anything.

Will do - I'm not sure if he's actually had a chance to take a look at it yet though, since he's juggling a couple different things at the moment.

While it did fix the map for me, now everything is super shiny, as if the ground was given a thin coat of lube.