FrodoBaggins: I'm using Windows 7.
But the browser shouldn't matter. Like I said, other sites work fine with IE11, so why not GOG?
I'm sure that has been said many times already, but IE11 is pretty much abandoned by MS at this point, as they are concentrating on Edge. Maybe they still deliver some security fixes to IE11, but that is all.
I've seen IE11 become broken on many other sites too besides just gog.com, e.g. a major Finnish news site where I regularly go. Sites just don't test their pages with IE11 anymore, they expect people to be using more modern browsers instead (like Edge, Chrome, Firefox, maybe Opera...).
I am also using Windows 7 at home, and I am using both Firefox and Chrome, never IE11 anymore after I started seeing it having compatibility problems on many sites. I use two browsers only because with some sites I want to retain cookies (like GOG.com so that two-factor authentication is never triggered) while with some I want cookies to be cleared every time I exit the browser.
For those "keep cookies" sites I use Chrome, while for those "clear cookies" sites I use Firefox, mainly because it is so easy to set up Firefox to delete the cookies and other crap when closing the browser.
As for Edge, I generally find it ok, but still I don't use it much. I guess I am more accustomed to how Firefox and Chrome handle bookmarks etc.