At this time, GoToWebinar is the only service that can stream a youtube video live. This may change in the future however, as services become more integrated with more shared feature sets.
However, you can stream a video directly from your desktop, if you use this method to stream the audio through GoToMeeting: https://support.goto.com/meeting/help/how-do-i-include-my-audio-during-a-meeting
@Peterzz I'm not sure if we've completed this feature in the new GoTo yet. Can you try going back to the last version to confirm?