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That's not how you restore a site in this case. 

Please follow the steps you see in the video tutorial Restoring a Site on Any Server. Outline:

• Delete all files and folders
• Upload the backup archive
• Upload kickstart.php
• Access the URL for kickstart.php

If you get stuck with a similar issue, follow the instructions in Akeeba Kickstart starts, but can't extract the archive, throws an AJAX Error, Invalid Archive Header or other error. The first two paragraphs apply to you.

Kickstart is an archive extraction tool, not a restoration script. The restoration script is ANGIE and it is included in the backup archive at backup time. This information is printed every time you run Kickstart and it is very clearly stated in our documentation and video tutorials.

Kickstart Professional is identical to Kickstart Core plus two additional features: import from URL and import from S3. You do not need to use Akeeba Kickstart Professional unless you need either of these two additional features. As per the information printed by Kickstart itself and in the documentation, the existence of these two features can be a security concern which is why you need to renamed kickstart.php of the Professional version into something else and use that instead.

Since you are not using either of these two feature you do not need to use Akeeba Kickstart Professional. Therefore, in the context of restoration, I cannot tell you what is the whole point of buying a subscription.

The subscription to Akeeba Backup Professional gives you access to Akeeba Backup Professional which has a number of additional features to the Core version including automation and storing your backups remotely. That is the whole point for most people purchasing a subscription.

It also has integrated restoration. And yes, we could have proceeded with that to begin with (you can change the timing options for the integrated restoration just like with Kickstart because, in fact, the integrated restoration does run Kickstart to extract the backup archive, just with a different interface) but what I was worried about is that your backup archive may not have been the same Joomla version family as the site you had backed up. This would have caused problems, as explained in the documentation. That's why I had you go through the safest option of using Kickstart.

Furthermore, as a subscriber to Akeeba Backup Professional you have access to Akeeba UNiTE (the automated, unattended restoration script) and support. So, if you're looking for a point to the subscription, we would not be having this discussion if you were not a subscriber. You'd have had to read the documentation where everything I told you can be found and which I can tell that you didn't want to.