No. Just move the files from the htdocs folder to the sudokusystem.com/htdocs. Don’t copy, don’t upload.
If you have the files and the database of your site, you have the entire site. All posts, pages, plugins, themes, settings are all contained in it.
That looks like a cPanel Full Account Backup. It can be used, but you’ll have to untangle the relevant files from cPanel’s somewhat cryptic backup structure.
If you still have access to the original hosting account, I would recommend just following our migration guide (and export your website files and database contents separately from HostGator).
If not, then know that everything is in the full account backup, it’s just a bit harder to work with as you’ll need to untangle the relevant files from the backup yourself.