Google Drive API - Downloading a file - php

Question

Using a oauth2 connection I have a working script (listing documents from Google Drive), I only need to add a download/export function.
Note: access_token / refresh_token are already set (different script)
//error_reporting(E_ALL);
require_once('vendor/autoload.php');
require_once('vendor/google/apiclient/src/Google/Client.php');
require_once('vendor/google/apiclient-services/src/Google/Service/Drive.php');
session_start();
$client_id = '<client_id>';
$client_secret = '<client_secret>';
$redirect_uri = '<redirect_uri>';
$client = new Google_Client();
$client->setApplicationName("Google Calendar");
$client->setClientId($client_id);
$client->setClientSecret($client_secret);
$client->setRedirectUri($redirect_uri);
$client->setAccessType('offline'); // Gets us our refreshtoken
$client->addScope("https://www.googleapis.com/auth/drive");
## Step 1: Set token ##
$array = array(
'access_token' => 'xxxxxxxxxxxxx', //set access token
'token_type' => 'Bearer',
'expires_in' => 0,
'created' => 0,
'refresh_token' => 'xxxxxxxxxxxxx', //set refresh token
);
$_SESSION['token'] = $array;
## Step 2: If token is active, list documents ##
if (isset($_SESSION['token'])) {
$client->setAccessToken($_SESSION['token']);
// Get the API client and construct the service object.
$service = new Google_Service_Drive($client);
// Print the names and IDs for up to 10 files.
$optParams = array(
'pageSize' => 10,
'fields' => 'nextPageToken, files(id, name)'
);
$results = $service->files->listFiles($optParams);
if (count($results->getFiles()) == 0) {
print "No files found.\n";
} else {
print "Files:\n";
foreach ($results->getFiles() as $file) {
printf("%s (%s)\n<br>", $file->getName(), $file->getId());
}
}
}
Unfortunately I'm unable to create a direct download link (for non public files). I have found the following documentation but I'm lost on how I can apply this:
https://developers.google.com/drive/v3/reference/files/get
https://developers.google.com/drive/v3/web/manage-downloads
The PHP example from "manage-downloads" results in an error:
Undefined variable: driveService in ... my_drive_script.php
Simply adding a link works, but only for shared documents (or if I'm logged in under the same user).
$fileid = $file->getId();
printf("<a href='https://docs.google.com/document/d/$fileid/export?format=doc'>Download doc</a>");
I have used the link format from http://www.labnol.org/internet/direct-links-for-google-drive/28356/
It should be possible to download non public files, right?