It's listed after Sargon of Akkad so I'm assuming it is the part of the list which is more or less historical.
It is indeed a fascinating line, and certainly captures at least a shadow of the uncertainty and anarchy in the last days of Akkad’s decaying hegemony.
Sargon of Akkad had united much of Mesopotamia into one of the very first true empires in history, by dint of his considerable force of personality and what scholars speculate may have been a standing army. A passing reference to “Five thousand men eat bread before [him]” is thought to refer to Akkad’s central military forces, though it may just indicate his broad-based support and authority.
The Akkadian Empire prospered for several generations, and Naram-Sin’s famous victory stele shows that the state was capable of wide-ranging military expeditions — and consequently must have had a robust administrative apparatus as well.
However, much of Akkad’s power was based, as one might expect, upon the fertility of Mesopotamia and the agricultural wealth provided by Tigris and Euphrates. Mesopotamia is not itself particularly rich in natural resources; it was its massive fertility that allowed it to become the heartland of a great empire, and gave Mesopotamian regimes the authority to acquire resources from outside the region. The copper necessary to make bronze, for instance, had to be imported. Many of Akkad’s military ventures may well have been large-scale plundering expeditions to acquire these resources, in a pattern familiar to us from the later Assyrian hegemony.
Toward the end of Akkad’s empire, things began to change rapidly. Drought and climate change began to weaken the supports upon which the empire was built; famine led to civil unrest and rebellion, which in turn exacerbated the famine itself. Akkad’s empire had replaced a system of locally powerful city-states constantly contending for dominance, and many of these cities survived as vassals under Akkadian rule. In times of distress, ambitious local governors and rulers rose up against the central authority.
Left to its own devices, however, Akkad may well have weathered the storm and re-organized itself to cope with its diminished resources. Many empires survived such crises throughout history, but things were complicated by the emergence of a new and deadly foe from the east. The Gutians seem to have been nomads and pastoralists who cut their teeth as mercenaries, and likely had a presence within the Akkadian empire long before the wars against them began. Libyans and Hyksos entering Egypt as mercenaries and settlers — and then ending as rulers — is an instructive contemporary example.
Although Akkad’s once-feared army no doubt resisted, the state was by this time under severe duress and seems to have lost control over much of its empire. This is where we get those lines about who and who was not king. Much as Assyria and even Rome experienced multiple civil wars and usurpations prior to their final collapse, so too Akkad seems to have a great many claimants contending for its throne.
This is surely a sign that no one king could command enough support over a long enough period to restore something resembling central authority — and divided as they were, they were unable to hold back the Gutian tide.
The Gutians ended as kings, though they did not govern well. Their contempt for and lack of understanding of agriculture meant that Mesopotamia suffered under their rule, although their ferocity and military strength served to keep Sumer under their sway for a considerable time.
Eventually, decisive leadership was found once again in Sumer — sparking a renaissance of that culture as the great Dynasty of Ur rose up against their Gutian masters and expelled the invaders, much as the Pharaohs of the New Kingdom would later expel the Hyksos.
Hope this was helpful!
Source: Marc van de Mieroop’s History of the Ancient Near East.