The basic premise of the article (that there are three distinct industrial revolutions with "fallow" periods dividing them) seems to me to be very easy to poke holes in. It's not as if some fundamental force of innovation switched on in 1760 and then faded away in 1830, only to reappear forty years later, as the graph in the article implies. Historians of globalization have been thinking about this stuff in a different way for quite some time now (for instance, Jan de Vries and his concept of a 17th and early 18th century "Industrious Revolution" is quite influential and has a lot of merit in my opinion).
It also isn't clear to me why the author(s) consider the automation of the 19th and 20th centuries, which they allow to have demolished entire industries and ways of life, to have been less threatening than the present wave of automation. Perhaps it has more to do with the fact that the people who write and read the Economist were those who benefited from the disruptions of the 19th and 20th centuries--and are now in a position to rationalize away their negatives--than with any qualitative shift in how innovation or automation is taking place.