They're specifically referring to the East Sea though, i.e. what the rest of the world calls the Sea of Japan.
the mighty East Sea...home of Dokdo...the most Korean place on earth
I put East Coast and it was right. For chinese speakers, this is literally 东海岸
Could this be just east coast?
Yes, "sea" need not be included, too literal of a translation.
동해 is the official Korean name for the sea that lies to the east of the Korean peninsula, but 동해안 was simply translated to "east coast" elsewhere in this lesson, and understandably so.