I dunno exactly how the big leagues do it, such as what tools they use, but I imagine they just have some sort of video-capture tool which is taking the view from the live game as it's running and then converting it into a stream which others can download or view. The easiest way would be to use something like FRAPS, use a video-authoring tool to edit it, and then stick it on YouTube.
Of course its possible and you only require one box watching within LFS to stream the data to the rest of the world (or to a dedicated box to save your bandwidth)