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I haven't used that script¹, but it looks like it duplicates both partitions into an .img file, then tar & gzips that. To extract the .img:

tar -xzf whatever.tar.gz

You can then mount and work with the partitions in the image following the instructions here. You can also use the .img to create an SD card following these instructions.

^{1. Because my answer to that question makes more sense ;) I explain there why dd is not a good tool for the purpose of maintaining a backup. I also explain how to restore from a backup using rsync...}