Both Natsuko and Chiemi are twin sisters, however both of them were seperated from each other since they were little.
Initially, Natsuko was really nice and friendly with Nobuaki and even nicknamed him "Nobu-kun" ("Nobu" and sometimes "Nobu-babe" in the English language) but constantly cheering him up, due to his tragic experience losing to all that matter in the King's Game before the events of Shuukyoku / The Animation, after both received an order from The King to kiss each other. Nobuaki refused to do so while Natsuko, on the other hand, did not matter seriously. Finally, after she found herself in the park, she managed to kiss him before midnight and revealed that she had fallen in love with him since the first time they met. However, after revealing her darker personality, she becomes sadistic, and self-centered. She is shown to do whatever it takes to survive the King’s Game, implementing brutal tactics to ensure her survival, in stark contrast to Nobuaki. In turn, Nobuaki tries his best to have her killed so she can’t harm anyone else. This puts a strain on the relationship between her and Nobuaki. At the end of the series, after mortally wounding Nobuaki, she explains that it’s better to kill the ones you love, [Nobuaki] than to let someone else do it for you, which makes it evident that her feelings for him were genuine. She dies saying the nickname she picked for him.
She loved Nobuaki because he reminded her of her old love who died because of the game.