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Yes, that definitely looks like a MAMP issue. Look at the error message. It says that it cannot find kickstart.php... which you are currently using to generate the page in which the extraction runs. It looks like something's breaking in MAMP under load and it can't figure out its virtual hosts.

No problem, though. Akeeba Backup archives include the restoration script. You don't need Kickstart to restore the site. Kickstart is only a tool to extract the archive. There's another tool which can do that, Akeeba eXtract Wizard, which runs as a desktop application and won't fail under load like MAMP.

SO, the best thing you can do is use Akeeba eXtract Wizard to extract the backup archive and then visit the /installation/index.php URL on that site to see ANGIE, the restoration script, and continue the restoration. When you're done you can delete the installation directory.

The database is inconsequential. When you are restoring the site you tell the installer (ANGIE) how to connect to the database. However, the error you posted had nothing to do with that since you had never reached that step.

Now that you gave me more information I understand what you did and why you had a problem. The problem was how MAMP was mapping your folder layout (on your drive) to domain names and paths in those domain names. This was caused by the .htaccess file of the first site you installed, inside MAMP's htdocs folder. This file screws up the way any other MAMP domain (with its web root created by default inside the htdocs folder) works. This happens because .htaccess files cascade based on the disk folder layout.

By moving your restoration target outside the htdocs folder you sidestepped this issue. The ~/Sites folder doesn't have a .htaccess therefore the restoration works just fine. The database has nothing to do with it.

Please note that our software works on a much higher level than the web server. Below our software there's PHP and below it there's the web server. I understand why you were confused that our software worked somewhat in your obviously wrong setup but there's nothing we can do to stop it and / or warn you. As a matter of fact the problem was caused by a file OUTSIDE the web root of the domain you were restoring to, i.e. a file that PHP itself won't let us see.