Are you sure you're using the correct version? Make sure you're using the "Latest Development Build" from the link I provided. It should say version 1.10.0. The latest stable build (version 1.9.0) won't support Riven at all. You'll still get the message that the game isn't supported, but it should work fine.
If you still have trouble (or you are already using the dev version), make sure all the required files are copied to the Riven install folder. I posted the link previously to that list.
Just to check, I installed the gog version of Riven last night. Currently running Win 8.1. It works fine. Got a bit of a glitch starting the game (gave me an error), but it started anyway. Played for a bit and didn't encounter any problems. Saves work normally. That is now 5 different systems with 3 different OSs that I've used the gog version on without problems.
I also tried the ScummVM engine to play it, and it too worked just fine. Actually it worked better as I didn't get that error message on startup.