Can humanity endure that transition, though? It'll take a while. Maybe generations. Some places will automate more quickly than others. And unless some means of providing for the now-unemployed masses is devised, and quickly, society and the economy will be crippled.
In the short term, automation means record profits for the capitalists who own the companies and machines, at the expense of all the people who get "downsized." Massive unrest. Combine that with all the drought, hunger, and overpopulation, and you'll see politics get more extreme, especially if First World machines take jobs from Third World people. Then we'll see a perfect storm. I could easily imagine populist leaders promise to drive out the hated machines, put people back to work, and aggressively assert their countries' water rights in disputed areas. As in, lots of war. It will at least serve as a smashing fiction setting...
Of course we can weather the transition. Much like the horse example in the video, our population will decline greatly. Is that really such a bad thing though? Given the strain the ever increasing number of humans is placing on just about everything from the economy to the planet itself, less humans walking around doesn't sound like a huge negative to me.