Although GOG doesn't offer support on older OS (XP, Vista), it is possible to have it running on XP, provided a small manipulation is done on one DLL. (taking a steam_api.dll from any Steam game, renaming it GalaxyWrp.dll and replace the one in the FNV folder by the renamed one). This will of course make Galaxy unusable.
Can't mark this as solved.
I can confirm this fix.
I was just able to install in on my XP box, cancelled out of installing the Visual C++ repair (I have Visual C++ 2010 installed), and hit the same error mentioned above (queryfullprocessimagenamea could not be found in kernel32.dll). Copying over the steam_api.dll (which IS compatible with XP) made it so both the game .exe or launcher .exe worked perfectly.
This confirms that the issue is that the Galaxy hooks for the game .exe's are the issue, NOT the game itself. In other words, Galaxy is not programmed to work on XP whereas Steam is.
I would look to this as a fix as I wouldn't hold your breath for GOG to make their Galaxy platform backwards compatible for XP.
To aid anyone looking to do this (and who can live with the loss of Galaxy functionality), I'm attaching the file here. Simply rename to the following (may be case sensitive) : GalaxyWrp.dll
The original file name exactly is : steam_api.dll
You can make a copy of the original file in case for some reason you decide to just move your installation to another computer rather than do a reinstall.
Good luck folks!