In the cited part on Emperor Chuai, his father YAMATO Takeru no Mikoto was called Emperor (YAMATO Takeru no Mikoto however never became an emperor in "Kiki" - Kojiki and Nihonshoki).
仲哀天皇の引用部分では、父の日本武尊が天皇と呼ばれている（『記紀』ではヤマトタケルは即位しない）。