I haven't tried this myself, but I see according the the WineHQ page for GalCiv 2 there appear to be varying levels of success from version to version. Here's the page:
http://appdb.winehq.org/objectManager.php?sClass=application&iId=3081
Hopefully that gives you some help, but I don't know what to tell you to do. Maybe somebody else will know better. You could try a GalCiv forum or an ubuntu forum. I find the folks over at ubuntuforums.org to be really helpful.
Good Luck