Look at how closely real wages track productivity growth in the U.S. (according to Stephen Gordon):
Maybe you expected a growing gap -- something more like this?:
The difference between the two graphs is largely a reflection of greater wage inequality ("the share of all wages accounted for by the top 1 per cent of wage earners has nearly doubled, from 6.8 per cent in 1973 to 12.9 per cent in 2010" - Mishel), the rapidly growing cost of health insurance and differences between the CPI and the GDP deflator.
When Stephen Gordon talks about productivity being "the only way for people to become better off" the naive assumption would be that he is referring to "most people" or the "average person" but the figures he uses to show that "market forces" ensure that "wages respond to labour productivity" have nothing to do with the average person (median) becoming better off -- they have to do with the wealthiest becoming better off and thereby raising the average (mean). Bill Gates walks into a room and the "average wealth" of the people in the room soars. He leaves and the average plunges.
Darrell Huff (1954) discussed this particular "average income" swindle in a whole chapter, "The Well Chosen Average" of his classic, How to Lie with Statistics. Compensation is not normally distributed therefore the means and medians are far apart. No doubt Professor Gordon will claim a plausible technical rationale for his use of "nominal compensation divided by GDP deflator." But such a rationale doesn't address the "why you should care" part.
Why should you care that the rich get even richer while the middle class stagnates? Well you should care but not for the reason Gordon implies -- that productivity increases will make you better off. You should care because the productivity gains of the last 40 years or so have done diddly-squat for the average sot. The rising tide has lifted the yachts. Period. Or, to express it in a chart: