Chapters 7 and 8 were not in chronological order. They happened while Belshazzar was still the king. Chapter 9 now returns to the events of the reign of Darius who became king in chapter 6.
This is background information about who Ahasuerus was. The UDB places this in parentheses to make that clear. (See: [[rc://en/ta/man/jit/writing-background]])
This can be stated in active form. Alternate translation: "who became king over the kingdom of the Chaldeans" or "who conquered the Chaldeans" (See: [[rc://en/ta/man/jit/figs-activepassive]])