You have got to take a look at the final graph in Thompson's piece, comparing "labor's share of the economy ... to corporate profits' share of the economy". In the late 1940s labor's share was modestly greater; by 1996 corporate profits had drawn even; after a brief resurgence between the late 1990s and roughly 2001, labor's share dropped precipitously while corporate profits went on a tear. After a severe hammering around 2008, corporate profits soared past their previous high in 2005-2006 and are still on an upward trajectory.
The most interesting thing about that last chart, by the way, is not the absolute value of current corporate profits; that number, indeed, is not all that far from its peak value in the late 1940s. The value of labor, on the other hand, has plummeted from its peak around 1970.
Taken together, these graphs don't tell us that corporations have utterly decoupled from the economy. When the economy crashes, we all crash together: corporate profits, employment, and growth. But when the economy recovers, we don't recover together. Corporations rack up historic profits thanks to strong global demand, cheap global labor, and low interest rates, while American workers muddle along, their significance to these companies greatly diminished by a worldwide market for goods and people.The well-being of corporations, in short, is only weakly tied to the well-being of flesh-and-blood people. So when anybody in Washington or on Wall Street points at corporate profits and tells you that the economy is recovering, it's quite rational to shout "Bullshit!" in reply.