There must be multiple social and environmental factors that have contributed to Italy being hit so hard (age of population, high rates of smoking and high levels of air pollution have also been suggested), but that could well be one of them.
People were going to work in Italy in non-essential industries until recently. Those workers went home to their aged parents. Countries with lower rates of working aged adults living with the elderly are likely to have higher infection rates of a particularly vulnerable age group than those where such living situations are less common.
Gonna wager a guess that there are vast amount of differences between South Korea and Italy that could affect the spread of a virus.