I install all my games as root, and have to jump through extra hoops to even allow games to write to the game dir (which they shouldn't be doing in the first place). Thus I have a complete list of files modified by the game (abbeycore.txt and files under userdata/Renowned.../ for this game).
Do you keep a list for other games too?
It might help me greatly in ./play.it
I have changed the way I do things. I used to log every written file (either by making the dir temporarily writable or using strace) and change permissions or make soft links. Now I just added a "-w" option to my game launcher script, which then uses unionfs to make it writable. I do something similar now on all my windows and dosbox games to keep the installation "pure", which doesn't always work well e.g. if a game opens every single file in write mode, causing my shadow copy to be a duplicate of the game. Currently I use that option on 15 "pure native" games, although some of that may be excessive.
Balrum - convig.xml, debug.txt, files/cache, files/saves
The Bard's Tale - I think it just tests for writability somewhere; it doesn't leave anything behind.
Bionic Dues - RuntimeData/
Call To Power 2 - ctp2_program/ctp/... actually, this isn't a GOG game, but the open source port of ctp2, which has numerous issues.
Eador Genesis - Eador.cfg, gamelog.txt, save/ (another non-GOG Linux binary)
Edna & Harvey The Breakout - actually, never mind on this - GOG has updated their version and I haven't retested.
Battlevoid Harbinger - in Linux64/harbinger_linux/ - save settings.xml user
Kerbal Space Program - a horrible mess.
Renowned Explorers - well, I already reported what I knew there. It obviously depends on what you do, and in what order, so some of my other reports here may be inaccurate, as well.
Rezrog - I think it just tests for writability somewhere; it doesn't leave anything behind.
Ronin - preferences.ini save.ini
All 3 of the Shadowrun series - DumpBox/ (this one always aggravated me the most, because I would forget to fix it and it wouldn't hang until any time a chapter ended).
StarBound - storage/*