It's good to read calm, reasoned comments on this from fellow posters who know about horses and dressage. It is not cruel in itself, nor is the proper and correct use of a lunging whip - which should not come into contact with the horse itself.
The clip is now widely available on many news and newspaper websites for anyone who wants to view it for themselves. I don't think anyone is trying to justify whipping a horse - as I've repeatedly stated on here, I would never condone any kind of cruelty to horses, but kneejerk reactions don't do anyone any favours.