My intuition is that reserve causality is playing a huge role in these numbers which is acknowledged by the authors:
"Why physical attractiveness should matter for intergenerational social mobility is an underexplored research question. Theoretical links between the two are complex, and the possibility of reverse causation cannot be ruled out. Prosperous economic conditions likely allow individuals to improve and maintain their physical attractiveness by investing in relevant services (e.g., quality hairdresser, gym membership, and plastic surgery) and goods (e.g., fashionable clothes and effective cosmetics)."
Cannot be ruled out strikes me as an understatement. I'm not sure what the exact design of the interview was, but even factors like how well-spoken someone is could have a strong influence on perceived physical attractiveness despite being heavily confounded by factors like education and socioeconomic status, which I think challenges the notion of physical attractiveness, as least as it was assessed here, being a truly independent predictor. I also don't think that this study serves as incontrovertible proof in support of the defeatist winging about how purely genetic factors affecting appearance have completely and unfairly hamstrung ugly people. A study that supported that notion wouldn't use an interview, it would just use a picture of people's faces from a standardized lighting and angle which would then be rated and correlated with these other variables.