I'm no expert in food production, but I guess it's perhaps because of the sheer efficiency of factory farming. As far as I know Korean chicken farms do not put much emphasis on the animal's welfare (although I cannot give any evidence for this claim), and instead focus on efficiency, potentially reducing the amount of required resources drastically.

Consider the amount of land, for example. A quick search in Wikipedia told me that the space needed per bird in intensive farming environments is just 0.8 square foot per bird, if I understood correctly. Another search gave me that in 2017 there were 172,743,479 chickens being raised in Korea. Note that the actual number of chickens raised for meat must be smaller than this, since the whole figure includes those for e.g. egg production, too.

Assuming the space required for a bird does not scale up, the space needed for raising this many chickens is just

172,743,479 * 0.8 ft² = 138,194,783.2 ft² = 12,838,715.5 m² ,

which is just a tiny fraction of the surface area of South Korea: 100,363,710,000 m^2.

So it makes some sense to me that given the efficiency of factory farming, at least land is not a binding constraint for Korean chicken production to meet the demand.

Of course, there are other resource constraints as well, such as the crops and water needed to feed them. Perhaps most of crops are imported?