No, you actually must not install Joomla! on the target server. The backup archive contains everything you need: all of the site files (including Joomla! and its extensions), the database backup and the restoration script which restores the database and reconfigures the site for use in the new server.
The only thing that you need to do before restoring the backup archive is create a new database. The restoration script is not given adequate permissions by your host to create a new database. This makes sense, it's a good security practice.
Nicholas K. Dionysopoulos
Lead Developer and Director
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