Thanks for your feedback. On Reddit another Vive user has the same problem. It might be related to Steam VR because I have the same problem when running the game through Virtual Desktop, which also uses Steam VR. I can see the controllers below between the chess tiles but they can't be moved.
I'm sorry the game doesn't seem to be playable on non Oculus headsets currently. I hope I find time to fix this soon but I'm busy with other features of the game.