I am pretty sure we have discussed this map before, but I cannot find it on this site. What do we know about this map and the mapmaker? I have a renewed interest in it.
I notice that many of the Japanese place names on the map are in katakana, including Matsushima (マツシマ), but Ulleungdo is labeled in kanji (竹島 -Takeshima). Likewise, other larger islands. such as Tsushima (對馬), are labeled in kanji, but their smaller, neighboring islands are generally labeled in katakana. Is it possible the mapmaker used a system whereby he labeled larger, main islands in kanji and smaller, nearby islands in katakana to show they were close enough to be considered neighboring islands of the larger island?
If such a system was used, maybe the "Matsushima" (マツシマ) on this map was not referring to Liancourt Rocks, but rather to Ulleungdo's neighboring island of Jukdo (竹島)? That would explain why the two islands are so close together on this map and similar maps and why Matsushima is drawn as one island instead of two.