For those still finding a tough time making this run in Windows 10, I came up with a solution (that works for me anyway) after trying to go through GOG support (they were responsive and helpful, but didn't quite diagnose the problem and solve it), I zeroed in on the 'Vista Fix' that has been mentioned here and elsewhere (Hawk and Badger for instance). Long story short (as I had to figure this out twice) the problem was as follows: RRT3 would launch fine the first time from the installer and then the dreaded directX error would ALWAYS prevent another load. The problem appears to be that the game unchecks the lighting whatever box when you exit and saves the engine.cfg that way. This causes the error next time. I'm nowhere close to an expert in programming/coding/etc, but I hope this helps someone who, like me, didn't want to install 2 or 3 other programs to download a patch, open it, install it, and then hope it runs the game. For reference, I use Windows 10, Intel processor i5, nVidia GeForce 730 card (nothing fancy by any means, but it works).
1. Do NOT install RRT3 through Galaxy, no matter what I did, it would never launch through there. Instead, download the 'backup game' installer from your account and run the installer.
2. Right click on the short-cut for RRT3 and choose 'Properties'. Click on the 'Compatibility' tab and choose an appropriate previous version of Windows from the drop-down tab. For me Windows XP SP3 was fine. Press OK.
3. I think the GOG version already comes with the 'Vista Fix' in place, but I'm not sure, so you may need the next step or not. Open the folder where you installed RRT3. Open 'Data' then 'Configuration'. Right click on the 'engine.cfg' file and choose properties. Check the box for 'Read Only' then press OK. From here you might be alright.
4. If not, get the 'Vista Fix' patch from Hawk and Badger. Right click on the download and extract all. Open the file until you find the 'engine.cfg.' Copy this file and use it to replace its counterpart in the RRT3 Configuration file. Now right click the file and check the 'Read Only' box and press OK.
At this point everytime I launch RRT3 from the shortcut, Windows asks if it's ok that it makes changes, so say yes to launch the game and away it should go. The game plays fine from here. The drawback (which maybe someone who understands this stuff better than me can help with?) is that it always loads in 800 x 600 resolution. You can change it to something else, but it can't save the setting so you have to change it every time manually (although I'm generally content at the 800 x 600). The important part is that it runs fine and saves games fine. I hope this is helpful, and if anyone has a better 'simple' solution (i.e. not needing complicated patches and programs just to open them), I'm all for it. Happy Railroading.