GOG: When we said we let you ‘own’ your games, we meant that no matter what happens you’ll still be able to play them thanks to our offline installers.
Installer file is a direct link to an executable file from their website. They contain the full game inside the installer. There's no reason you can't download that on Linux as long as you have internet and a browser.
GoG homepage > (your name [drop down menu] when logged in) > "Games" > Click on any game in your collection > Download offline backup game installers
You can download installers for whatever systems the game supports -- usually that's just a Windows .EXE installer (+ several .bin files if the game is large). For games intended to run on Linux w/o WINE, you can select "Linux" from a drop down where it says system and it will give you an .sh file.
If it's an EXE and you just want extract it you can use https://github.com/dscharrer/innoextract
It supports the special GOG Inno files. And it's a lot faster than the official installer with less temp files.