As shown on google data provided samples you can parse the video after the upload process is completed. Regards
ru.AsyncOperationCompleted += new AsyncOperationCompletedEventHandler(ru_AsyncOperationCompleted);
void ru_AsyncOperationCompleted(object sender, AsyncOperationCompletedEventArgs e)
{
//upload complete
YouTubeRequestSettings ytSettings = new YouTubeRequestSettings("myApp", googleDevKey, ytUsername, ytPassword);
Video v = ytRequest.ParseVideo(e.ResponseStream);
string videoId = v.VideoId;
string watchPage = v.WatchPage.ToString();
}