The "fault" lies with the engine the browser uses -IE uses Trident, while Chrome uses WebKit and Firefox uses Gecko. The latter 2 are now well supported by the majority of websites, and Trident support was dropped. Edge (the IE of Win10) uses another rendering engine, more similar to WebKit than Trident, and thus renders things correctly.
P.S. If you want to further see what I mean, you can try out Lunascape -its a browser that includes all 3 rendering engines but uses Trident by default. With Trident GOG's homepage looks awful , but with WebKit/Gecko it looks just fine...

Explorer 11 uses the Edge engine by default (though I'd guess it hasn't been updated for a while), but can be set to use a version of Trident either by using compatibility mode or by choosing an earlier Explorer version through the developer panel.

I haven't experienced any problems with Explorer 11 and GOG (though I rarely use that browser here, partially because I'm rarely on a Windows machine, and even then I prefer Pale Moon).

Aren't you explaining too much to someone who's still using IE in 2016? :P

Just tell him:
IE11 isn't supported anymore by many websites, you'll have to switch browser.

Well, he might not like the layout of the other browsers -which is the reason I use Chrome rather than Firefox - I prefer Chrome's layout and bookmark management over Firefox's (Firefox does have some other nifty features though, so I keep both installed...). Which is why I proposed Lunascape, which I myself tried a few days ago (in my perfectionist quest for the most lightweight browser) -it looks like IE, but its Trident is slightly more lightweight than IE's and if he uses Lunascape with WebKit/Gecko he will have a better rendering with the exact same IE-look-alike browser. Also, this stuff is not too complicated - I have not studied CS or anything like that at all so it's not like I breath tech...

Works just fine for me, also using IE11. Any specifics on what exactly doesn't work? Any error, screenshots of how messed up it looks, something?

*growls at phaolo*
Me, I won't be touching Chrome, and can't see myself using FF on a regular basis at all, only have it there for a few cases that cause issues in IE (usually due to odd ads or many scripts running on the page, which are usually also for the ads, blah - those make IE work sluggishly or even crash) and for times when I deem a place too risky to load it in my regular browser. Vivaldi may be an option, gave it a spin and seemed nice and ticked almost all the right boxes, but being based on Chromium makes me wary even if it's not actually Chrome, and they have some stuff to iron out still.