Ah. Confusion. I see it.
You are supposed to install to /zenphoto, not `/zenphoto/zp-directory`
"[zp-directory]" in the installation literature refers to the [i]directory where you are installing zenphoto[/i], not to a directory named zp-directory.
Please copy the files such that the `index.php` file is in the root `/zenphoto` folder, and the `zp-core` folder, `albums` folder, `themes` folder, and `cache` folder are in the `/zenphoto/` folder on your server. They should not be in any subdirectory.
Just to be [i]completely[/i] clear, this is how the file and folder structure should look:
/zenphoto
--> index.php
--> rss.php
--> [i](a few other .php files)[/i]
--> /albums/
--> /cache/
--> /zp-core/
||--> zp-config.php
||--> template-functions.php
\\--> [i](A lot of other .php files)[/i]
--> /themes/
There may be more files and folders, that's just to give you an idea of how it should look.
Once you have it extracted correctly the error message should disappear, but come back if you have more problems. Good luck.