Awful take. For starters, GOP-dominated counties tend to have smaller populations, which means less available labor to exploit for profit, and fewer jobs - of fucking course their GDPs are going to be smaller! What is even the point of looking at aggregate GDP (which corresponds to local capitalist profits more than anything worker-related with the post-1970s wage-productivity divergence), and then drawing a conclusion about the work ethic of the average person in each county? This person isn't even citing per capita data, which would control for the fact that there are just more people in the dense urban counties where, of course, Dems tend to do better!
(Relevant xkcd: https://xkcd.com/1138/)
If they wanted to make a point like "Republican voters don't work", they should have looked at unemployment insurance claims by county, or any of the U3, U6, or labor force participation rate. Most of these data should be available from the BLS.
Regarding the Brookings Institute article that produced this infographic, which has its own different problems, they use this statistic to comment on the same old portrait of a rural-urban economic divide manifesting in divergent propensities to support different parties, aka shit we knew already (with some classic conflation between Dems/libs and the left-leaning voters they hold hostage):
The problem—as we have witnessed over the past decade and are likely to continue seeing—is not only that Democrats and Republicans disagree on issues of culture, identity, and power, but that they represent radically different swaths of the economy. Democrats represent [sic] voters who overwhelmingly reside in the nation’s diverse economic centers, and thus tend to prioritize housing affordability [sic], an improved social safety net [sic], transportation infrastructure [sic], and racial justice [sic]. Jobs in blue America also disproportionately rely on national R&D investment, technology leadership, and services exports.
By contrast, Republicans represent an economic base situated in the nation’s struggling small towns and rural areas. Prosperity there remains out of reach for many, and the party sees no reason to consider the priorities and needs of the nation’s metropolitan centers.