Watching Youtube Videos after they've been uploaded is technically streaming those videos because the video is being constantly downloaded to your computer or device while watching so it's indeed streaming video.
But when you watch Live TV or are streaming live videos then that's what is really considered to be streaming but either way you're still streaming videos when watching Youtube whether you watch the video after it's been uploaded or when you're watching a Live Video being streamed.
So yes watching videos on Youtube does count as streaming.