Have you tested other software supporting the Vive?
Yes have several other games that work fine, but not sure I can think of a Vive title that uses a menu like KRPs, i.e. a floating game menu in the Vive default VR area (not sure how relevant that might be?). I think every other Vive title launched from SteamVR was while wearing the HMD and most use the tracked controller as a pointer, no mouse needed. Only other non Steam title I've used is Live for Speed but I can't remember how the menus worked (no tracked controllers so must have been mouse) as it was a while ago, but it worked fine. Can test later.
Should KRP start fullscreen?
A 360 KRP dome instead of the default Vive one would be handy but not essential, if that's what you mean. Initially after launching KRP I wasn't sure it had launched into VR because as said it put the menu way to my side, and side on that 2d menu was not so easy to see. So a branded 360 dome would make it obvious. The only other clue that it's launched in VR mode is that the desktop game screen although blank was in windowed mode. Thinking of spectating, will the desktop window show the game once playing? It isn't showing the menu currently.
Just read the Rift supports the demo too, so i'll try that later to see if it's the same.