Japan and Korea are more or less on the same latitude and near each other and Japan has slightly more area than Korea. I doubt this is an issue about projection distortion.
The mercator projection is a projection...a mathematically consistent way of displaying the surface of a sphere as a two dimensional image.
This map is something else entirely. Not even sure what to call it, but it isn't a projection. The korean peninsula is bigger than India. It's a fantasy at best.