Productivity is based on the value of the work done, not any profitability assessment. The original post which set off this chain asserted it was about not how much workers get done but how much money is made off of what workers get done ... which is unambiguously wrong.
I don't believe the difference is consequential here, since the originating point still holds even using your definition. I wouldn't say it's "wrong" so much as imprecise, as the way I interpreted the statement would encompass your more detailed description.
It's like when I ask people "how much money" they make, I intend them to include non-cash compensation in the number (in dollar equivalent), and pretty much all do without additional prompting.
I was playing loose with the jargon meaning for sure, but I'm pulling out to what articles in the Washington Post or other economics-focused media really care about: the impact to corporate bottom line.