I found a helpful Reddit post that details a method of playing Riven on modern operating systems (Windows 10 for me) and it works like a charm so far.
Here is the post: https://www.reddit.com/r/myst/comments/3k0xvd/psa_you_can_run_riven_perfectly_fine_on_newer
I will paraphrase what he tells you to do as well as including some additional steps that I needed to take to make it work with the GOG version as his version assumes you have the game on CD/DVD.
1. Download a ScummVM nightly build. The build I downloaded was right at the bottom, Windows (64bit), and I downloaded the latest development build rather than the latest stable build (the stable build kept saying I was missing data files so I was unable to launch the game). Drag the folder from the zip to your desktop or wherever you prefer.
ScummVM builds download page: http://buildbot.scummvm.org/builds.html
2a. Check that you have the necessary data files in one folder, which for me was GalaxyClient/Games/Riven/Data. You should have all the files you need (ignore the optional ones) barring one, which we will cover in the next step...
Datafiles list: [url=http://wiki.scummvm.org/index.php/Datafiles#Riven:_The_Sequel_to_Myst]http://wiki.scummvm.org/index.php/Datafiles#Riven:_The_Sequel_to_Myst[/url]
2b. Copy or move your Riven.exe file into the Data folder.
3. Open the ScummVM folder we extracted earlier and run ScummVM. Select Add Game and navigate to your Riven folder, select the Data folder and press choose. (You don't need to go into the Data folder, just select it).
4. Now select the game in your ScummVM main menu and press start. To play the game in fullscreen, press Edit Game, go to the graphics tab, tick override global graphic settings and then tick fullscreen mode. Press F5 in game to bring up a menu which allows you to save, load and quit. Also a nifty feature of ScummVM is that you can press F4 and it draws the selection boxes around the clickable zones in the game.
If you press start and ScummVM tells you that you're missing files, double check that all the files you need are in your Data folder (remember you need Riven.exe in there too). What solved it for me was trying out different ScummVM nightly builds, trying both 32 bit and 64 bit, stable and development.
I hope this is helpful to people, I know it's not the perfect workaround but if you've exhausted a lot of options then ideally this will be what you've been looking for. Happy adventuring!
The problem here is it is no longer GoG. It is ScummVM.
I do have the same problem where it launches, changes resolution and then closes.