You say you included class-wp-upgrader.php, but the Codex page for request_filesystem_credentials() indicates that the function is defined in /wp-admin/includes/file.php. That’s the file you’d need to require() before you can use it.
Looking at the source of class-wp-upgrader.php, the request_filesystem_credentials() function is part of the WP_Upgrader_Skin class, not a standalone function. There’s no guarantee that WP_Upgrader_Skin::request_filesystem_credentials() does the same thing as request_filesystem_credentials(), either.