Koreans try to make the definition of Korean as wider as possible. They believe Bohai (Balhae in Korean) was a Korean state.
Subsequent to the fall of Goguryeo, Dae Joyeong, a former Goguryeo general, formed an army of Goguryeo and Malgal (a Tungusic tribe) people, and led a migration to Chinese-controlled territory. They settled eventually near Jilin in Manchuria, and there founded a state which was at first called Jin, but in 713 was renamed Balhae (Bohai in Chinese). Balhae soon gained control of most of the former Goguryeo territory. The ruling class of Balhae consisted mostly of Goguryeo (i.e. Korean) people. Balhae declared itself the successor to Goguryeo, and sometimes called itself Goryeoguk (state of Goryeo).Korea.net: History: The Balhae Kingdom
It is interesting Koreans think that Gaogouli (Goguryeo) people were Korean and that Mohe (Malgal) people were not Korean. This is questionable because Gaogouli and (Old/Middle) Korean share only few words. Even if their claim holds true, Da Zuorong (Dai Joyeong), the founder of Bohai, was not Korean. He was a chief of Sumuo, one of a Mohe tribes and Sumuo tribe had been under the protection of Gaogouli. Therefore some history books say he had been a Gaogouli general and others say he was from Sumuo Mohe. That is all.