As I read it, they didn't even measure working hours directly because "we have another issue in examining the
effects of labor hours on cognitive functioning, that is, labor hours are censored (that is, retirees report zero working hours). Rather than directly using variables which correlate with labor hours, but do not correlate with cognitive functioning, we use these variables
for creating the fitted values for squared of working hours and working hours as instruments."
And they run a regression to infer working hours from the region they live in, parent being alive, number of children and so forth.
Let me just get to the main point: I think they're just picking up a decline in cognition from lack of sleep. If someone is stressed out with all these obligations, then longer work hours will cut into their sleep.
Also, I don't see how they figure out which way that causality runs: could those who have good cognitive function afford to work fewer hours than those who don't?