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That's a PHP configuration setting, which your hosting company needs to fix. Ref: http://php.net/manual/en/zlib.configuration.php

Okay. Ask your hosting company to explain why their PHP 5.6 configuration doesn't handle standard PHP OOP syntax.
This is a server issue, not a Zen Cart issue.

Please post the top 80-100 lines of information from the phpinfo() output you added to zc_install/index.php

I'm pretty sure that's not what your Zen Cart folder is using. Otherwise you wouldn't get the message you're reporting.

To find out what specific PHP setup is actually being used, edit your...

There's nothing wrong with the syntax in the file. See line 20 here: https://github.com/zencart/zencart/blob/v155/zc_install/includes/classes/class.zcConfigureFileReader.php

Agreed. It's rejecting the PHP keyword "protected", which was added in PHP 5. So that means the site must be running an ancient version of PHP.
You'll need a modern version of PHP (5.6 is...