I little elaboration on your post.
The new directory cannot replace the original director because of a disk malfunction.
Since the drive is physically bad, DiskWarrior is refusing to write the optimized file table to disk since it's highly likely it would be corrupted while doing so. Which means a bad situation would instantly be much worse.
Then it says "It is highly recommended that you back up all of your data from the preview disk."
The Preview Disk is a pseudo representation of the repaired drive before the data is actually written back to disk. It wants you to save your data from there since it's more likely to correctly write the files you're saving to the backup device.
Now I'm at the preview screen and it's a split type screen.
Back out of the split view so you can mount your external drive. Click the option to view the repaired drive and copy from there.