I'm having the same problem, but on Mac OS 10.8.5. I was running the free version (4.2), but decided to buy a copy. I deleted the free version from my Applications folder and installed Sweet Home 3D from the App Store, but I now get the same problem as the OP.

I then deleted the new version, went back to the App Store, and reinstalled the app, but got the same result.

Has anything new come to light about this?