Though generally we should all be all in favour of going back to the original documents the English google translation (of the original German) to which your question provides a link is not of good enough quality to get much information out of at all.
In this linked Wikipedia article the nature of the case is stated very plainly... https://en.wikipedia.org/wiki/Ferdinand_Hitzig
Apologies to purists who want original work on stack exchange but I am going to simply cut and paste the wiki article, not least because it is possible the wiki article might get deleted or altered at some time in the future:-
"It has been charged that certain "fundamentalists" were wrong in citing Hitzig as an example of those who denied the historicity of Belshazzar. But Hitzig really did hold the erroneous position ascribed to him by conservative scholars, as shown by what he wrote in his commentary on the Book of Daniel.
Selbst den Fall gesetzt, dass der fragliche Koenig Mediens existiert habe, wurde der Name, unter welchen er bei Daniel auftritt, zu beanstanden sein. Jene zweiheit in Nabonned = Baltasar wiederholt sich in Cyaxares = Darius, und wieder zu Daniels nachteil.[1]
["Das Buch Daniel", 1850, page 77]
Translation:
Even supposing that the king of the Medes in question [i.e., Darius; Dan 5:31] had existed, the objection is the name under which he is referenced in Daniel. Each of the two were standardized in Nabonidus = Belshazzar which is repeated in Cyaxares = Darius, to Daniel’s discredit.
Hitzig thought that, historically, there was no such person as Belshazzar, or alternately, that the deluded author of the book of Daniel made two mistakes: he gave Nabonidus the name Belshazzar and Cyraxares the name Darius. Hitzig's position logically followed from his presupposition that the book of Daniel was a fraud perpetrated by a nameless author in Maccabean times. Such a deceiver could not have known a genuine name of Belshazzar from the sixth century BC, because at the time Hitzig wrote, all resources available to him outside of the Bible and texts derived from the Bible named Nabonidus as the last king of Babylon, without any mention of Belshazzar. This conclusion was therefore a natural consequence of the starting assumptions, which were the presuppositions accepted by the radical criticism of the day. As the Jewish Encyclopedia explains:
The name "Belshazzar" was previously held to have been invented by the author of the Book of Daniel, which has long been recognized as a Maccabean production (see DANIEL). Since the discovery and decipherment of the cuneiform inscriptions, however, "Belshazzar" is now generally admitted to be the Hebrew-Aramaic equivalent of the Babylonian form ‘Belsharuṣur’ (Bel preserve the king), which has been found in the cuneiform documents as the name of the eldest son of Nabonidus (Nabuna'id), the last native king of Babylon (555-538 B.C.).[2]
[The Jewish Encyclopedia, "Belshazzar" (NY and London: Funk and Wagnalls, 1909).]
A modern evaluation of Hitzig's scholarship should take into consideration not only his starting presuppositions, but also how the deductions from those presuppositions have led to numerous errors in judgment that have later proved to be unsustainable.
It seems Hitzig was guilty of that most common fault amongst "scholars".. giving more credence to evidence external to the Bible than to the Bible itself.
