Zenphoto runs fine in the root of a webspace domain actually and must not be installed in a folder. If it doesn't you will have to review error logs. Or since Arvixe advertises Zenphoto hosting you probably should ask them why this doesn't work.
My initial guess is that something is wrong in uploader.php in the line that zenfolder is checked and when there is no zenfolder rather than the root directory it fails.
The uploader does not require a "folder", it uploads to the albums folder. But you have to create albums within that, you cannot upload direclty to it.