PHP MySQL is a deprecated database interface, so Zenphoto is attempting to migrate your installation off of it. (PHP MySQLi is the replacement) The underlying database is the same, so if the credentials work for one version of the interface they should work for the other. Apparently, though, there is some possibility of a mis-configured PHP MySQLi. But we have no clues as to what has been done wrong.
Probably your best bet then is to disable the mysqli extension in you PHP ini file until it is properly configured on your site. Your other option is to remove the `functions-db-MySQLi.php` script from your install. But this will be something you will have to do each release and Setup will complain when it finds it missing.