This is the definition of historical records.
What you said about China's first history book is too general, because there are many kinds of history books, such as:
China's first chronological history book was Zuo Zhuan?
China's first national history book was Mandarin?
China's first biographical history book is Historical Records.
China's first dating history book was Hanshu?
Therefore, Historical Records is not the first historical book in China, but its name is Historical Records, which is not a generic term.