The video shows a brief shot of their source:
A quick search reveals this CBNC article:
In a new paper, Federal Reserve Bank of Atlanta economists Julie Hotchkiss and Melinda Pitts found that smokers only earn about 80 percent of what nonsmokers earn. People who used to smoke and quit more than a year earlier, though, earn 7 percent more than people who never lit up in the first place.
The two researchers attribute about 60 percent of the wage gap between smokers and nonsmokers to demographic differences—collectively, smokers tend to be less-educated than nonsmokers, for instance—but the rest were ascribed to what they called, "unmeasured factors."
"The wage disadvantage to smoking has been well documented … [but] hard to believe that the direct unpleasantness of smoking is the main factor," Frank Stafford, an economics professor at the University of Michigan's Population Studies Center, said via email.
So, yes, there is a wage gap, but most of that wage gap is not caused by smoking.
Newspapers aren't reliable reporters of science, so let's go to the original paper:
Note: Working Papers are typically not considered peer-reviewed.
This paper finds that nearly two-thirds of the 24 percent selectivity-corrected
smoking/nonsmoking wage differential derives from differences in characteristics between smokers and
nonsmokers. These results suggest that it is not differences in productivity that drive the smoking wage
gap. Rather, it is differences in the endowments smokers bring to the market along with unmeasured
factors, such as baseline employer tolerance. In addition, we also determine that even one cigarette per
day is enough to trigger the smoking wage gap and that this gap does not vary by smoking intensity.
The lack of a dose-response curve is more evidence against causality.
The paper discusses the possible reasons for the correlation. It does not claim causality. It does suggest that, perhaps, it is the employers' perception of the smoking employees that is the major factor.