You don't have to start the game over. In fact, I recommend against it. This bug, although serious, doesn't affect your villagers or your tech. You should be able to finish all of the "lost" puzzles much more quickly than you would if you were starting over.

We believe that we have found the cause of the bug (a timing problem with the game's autosave function), and the fix will soon go into testing. It is unlikely to occur twice in the same game, but there is a foolproof way to prevent it from occurring until the fix is available: make a quick backup of your savegame files before launching the game. That way, you can put the game back the way it should be if something bad happens.

You can find the backup and recovery procedures here.