There has been extensive debate around that topic since that paper came out. Some points to discuss:

1. Even the article you shared mentions that starting in 2003, earnings has stopped tracking productivity. "Total compensation remains close until 2003, but does not follow 2003’s uptick in productivity growth (behavior which remains a topic for future research)."

2. They use average earnings and not median earnings. Average earnings include people like CEOs. This by consequence shows that inequality among workers has also increased. Check out chart 4 here to see how much smaller median wages are compared to average: (https://www.csls.ca/ipm/23/IPM-23-Mishel-Gee.pdf)

3. Apart from the average vs median difference, the biggest point of contention between that study and more recent ones is the measure of inflation used. The 2007 study you cite uses a measure of inflation that also includes things paid by employers like medical insurance. It turns out that using that one leads to significantly lower inflation. If you use consumer price index, what workers actually pay out of pocket, the difference again becomes larger. Citing page 37 of the study above: "In other words, that the prices of consumer items has risen faster than a broader index of prices that includes net exports, government goods and services, and investment goods. Therefore, for a given increase in income, the purchasing power of the consumer has fallen faster than that of business for investment goods and foreigners for U.S. exports."

The article I shared before plus this other one describe all the discrepancies (https://www.epi.org/productivity-pay-gap/). Specially see chart 10 in the PDF study. That shows all possible variations of how you measure productivity and income. No matter how you look at it, the most substantiated conclusion is that income has NOT matched productivity.