Make sure you are using the correct OAuth scope - the scope in the code above is for the Google Prediction API. Use https://www.googleapis.com/auth/bigquery
for full access to the BigQuery API. More about BigQuery API authorization here.
Example:
$client->setAssertionCredentials(new Google_AssertionCredentials(
SERVICE_ACCOUNT_NAME,
array('https://www.googleapis.com/auth/bigquery'),
$key)
);