The way you do this is to upload that tar.gz tarball up to your user space then log in to the shell via ssh and expand the file using the *nix tar command. I’m assuming you know how to ftp, as you have gotten this far, so I won’t address that further.
Read the Dreamhost Wiki Article of the shell, paying special attention to the included links to “enabling shell access”, to make sure that your user is authorized to access the shell.
Once you have connected to the shell, and can see your newly uploaded *.tar.gz file, you can “extract/expand” that file into you space with the “tar” command.
For more details on the use of tar, just type “man tar” and the tar user manual pages will be displayed.
Once your tarball is expanded, you may have to move some directories around, or rename some directories, depending upon the structure of your site on the other host, in order to have the files in the right place on DH ’ structure.