score:7
The short answer is, the historical list (i.e. the image in the question) provided with the year-stamp is not really showing the chronology properly. The key point is Chen Shou's Records of the Three Kingdoms, although written in the 3rd century, should be correctly stated as "annotated & compiled in the 5th century" (by Pei Songzhi). So, it should show:
If it was stated this way, it should clearer, that Chinese historiography during the early years did not progress smoothly, with big and inconsistent gaps when the official history was finally adopted.
Longer answer:
The longer answer is Chinese historiography during the early years went through substantial changes in approach, philosophy, etc. A few points about the key texts in question:
First, the 2 books on Han dynasty, Book of Han (by Ban Gu, referring to Western Han & Wang Mang) and Books of the Later Han (by Fan Ye, refering to Eastern Han) are actually mostly from Ban Gu. Fan Ye's Book of the Later Han is, in part, based on the work of Ban Gu, i.e. from Dongguan Hanji (東觀漢記).
Second, Ban Gu, the historian for Han period, was imprisoned and died (92 CE) before he could complete his work, i.e., complete his unified Han Dynasty history. His sister, Ban Zhao, helped complete the Book of Han -- the Wikipedia entry shows this.
Finally, to understand the context of Chen Shou's work, Record of the Three Kingdoms, it is better to see it as a very basic work (not really good enough as historiography) and needed Pei Songzhi to help complete it, see: Annotations to Records of the Three Kingdoms.