A refutation would be explaining why GDP and income don't necessarily correlate, which is more a matter of accounting identities. Specifically, GDP != income, income is merely one component of it.
It's quite easy to see that even if GDP grew 12% as someone else mentioned, the change from 64% to 57% would keep incomes at approximately the same level (and perhaps even slightly lower).
Wage share is an economically accepted term, with data from BLS behind it.
You literally made up some number and said "it doesn't change much over time".
You're going to need to provide a source for that 80%.
http://www.bea.gov/newsreleases/national/pi/2016/pdf/pi0716....
and GDP in current dollars was 18036.6 billion - http://www.bea.gov/national/xls/gdplev.xls, so 87.5% of GDP was income, and that figure has been pretty much constant over last 50 years, at never out of 75-90% range for sure. In fact, it is higher than average in the last 10 years or so - while difference is really small.
Disposable income after all taxes and including all social transfers (excluding non-monetary ones like food stamps and assisted housing) was 69.5% of the GDP, also quite typical figure which shows to tendency to fall over time, more likely to rise.
Surely that includes dividends, rents, and realized capital gains. And yet, it must have been reflected in the chart in question, if only in the top decile - while chart somehow shows incomes of all deciles falling from 2000, which is hard to believe.
Since personal income includes capital income, that's a useless figure when "wage" is being used as an (admittedly, imperfect) proxy for labor income as opposed to capital income, as the context upthread makes clear it was.
This is a main point in Capital in the 21st Century by Thomas Piketty. He explains the capital/income ratio and its effects on the economy. Decent write up here: http://www.robertdkirkby.com/blog/2015/summary-of-piketty-i/
No chart is ever data. A chart, like the result of an SQL query, is a projection via analysis. The analysis may be trivial, or it may not. You can hide a lot in non-trivial analysis if you want to. I don't say that the NYT did so here (and I don't say that it didn't), but it's hard to have any kind of productive discussion when something this basic is overlooked.
Also... You don't "trust" that chart? You can probably calculate it yourself if you want. That chart is data. If you have any reasonable arguments against the accuracy of that data Id love to hear it.