And the fact that all lengths are multiple of 600, is even more telling knowing that they counted in base 60
The mathematical and astronomical tablet texts we have of Mesopotamia, where we understand the numbering very well, are much later, in Babylonian Akkadian from the 5th century BCE.
Could be a simple misunderstanding as interpreting something that was intended to be metaphorically read as "quite a long time". Like myriad - literal translations might yield Chinese historical texts claiming unlikely numbers in multiples of 10.000 when the author might have intended to say just "very, very large number, beyond what we have seen around here in living memory".
From what we gather, around 2300/2200 BCE the very first territorial empire known, the Akkadian empire rose and then fell. There's a great book about it called "The Age of Agade". Enheduanna, thought to be a daughter of one of the Akkadian rulers, is one of the oldest authors known! She is thought to have authored some poetry we've found from back then. After the Akkadian territorial polity fell, southern Mesopotamia fragmented into city states and that is when these 'king list' tablets are thought to date from.
Note that the odd precision is due to just a single entry. Remove that entry, and pretty much all of the old entries are either perfect squares or nicely round numbers in their numeral system.
There's always the possibility that it is just some mythology without deeper meaning, that it represents garbled memories from pre-literary times. It might be encoding something we don't understand or just collectively misremembered stories or even just gibberish that came to be seen as significant purely by tradition or repetition.
We don't really know all that much about these peoples who lived at the early stages of our current post glacial stage of human society. We have a lot of data, to be sure, but very little in the way of a coherent interpretation for it all. In fact, the vast majority of the cuneiform tablets that have been digged up haven't even been examined properly yet, as in transcribed, translated and analyzed.
We have a few glimpses of the culture of Sumerian and some of it is this odd lists of names and numbers. I mean, even calling them "kings" is anachronistically projecting a very recent concept of Medieval Europe into a past at least 3 times as distant from as as the very earliest tribal leaders that came to be termed 'kings'. One common title used translated as 'king' (I am not sure it is written in these name lists) is lu-gal. It means 'big man', or magnate.
Hell, Sumerian is a language isolate. We interpret it largely based on context from later vocabulary borrowed by Semitic languages such as Akkadian and more recent descendants in Assyrian, Aramaic, Hebrew, Arabic and so on... Studying ancient Sumer and ancient Egypt is very very close to studying alien societies. We share very little with them other then happening to inhabit the same planet. We only understand Egyptian writing because some stone inscription had the same text in common late antiquity Greek, and ancient Egyptian written in hieroglyphics, and a script believed to be its more 'cursive' form.
I know this must somehow explain the giant numbers but I'm still not sure how precisely.
Counting in base 60 would make for much smaller numbers, no ?
For example, the number 16 in base 2 is 1111. but in base 10 it is 16. Ergo smaller base, larger number, and vice versa.
So did you mean to say they counted in units that are made of 1/600 of our solar years? I think that would make more sense, putting their reigns between 31-72 years of our counting.