This is a map "STANFORD' MAP: EASTERN CHINA, JAPAN, AND KOREA" which was published in London by Edward Stanford in 1904 during the Russo-Japanese war.
Although the islands in the Japan Sea were not coloured, they were labeled with Japanese names in parentheses - Argonaut I. (Taka Shima) which was a phantom island, Dagelet I. (Matsu Shima) which was true Ulleungdo and Hornet Is which were Liancourt Rocks. One can't say sovereignty of Liancourt Rcoks from this map but it is possible that they were thought to be Japanese territory because the name of Ulleungdo was labeled in Japanese as Matsushima (Matsu Shima) and in these cases almost all of them indicated Matsushima and Liancourt Rocks to be Japanese territory.