Or even the much later Russia under Ivan the Terrible was ungodly big. Was the river network just that effective at allowing such large & centralized states?
If so, when did the rivers stop being able to keep up with the West and Russia become a backwater?
The Kievan Rus was not a centralized state, in a way it was not even one kingdom or such. The ruling dynasty of the Kievan Rus were the Rurikids, a very big noble house originating from Scandinavia like the warrior-merchants that built many distinct principalities in regions that were mostly populated with Slavs and Finns. We don't know much about these populations but they didn't seem to have organisations that could compete with the Rus or waragians, as the scandinavian merchant were called. These many principalities were ruled by princes of the Rurikids in a succession that sorted the successors by age and the principalities by value. So there were a steady line of successions until you came to the Grand-Duchy of Kiev that was the most valued of these principalities. Holder of Kiev was the de-facto ruler of the Kievan Rus, the Grand-Duke of the Kievan Rus. You can imagine that such a system had many problems, as lesser principalities were easily discarded for more prestigious ones and so a prince were seldom interested in seeing to increase the wealth of these regions. Also, the actual form of governance could vary too, as the rich city of Novgorods proved, being more of a republic with the prince being mostly the leader of the army.
The power of the Great-prince outside of the now-Ukraine was strenuous at most and mostly relied on wealth through the trade along the Dniepr, but the dynasty of the Rurikids proved to be very vital and popoulus, surviving the christianization and even their century-long vassalization. After the defeat to Batu Khans Golden Horde 1240 the Rurikid dynasty was under the overlordship of their Khan, the great-principality had to be appointed by him (for hefty tributes of course) but the Khanat was never interested in a restructuring of the Rus, while in the now Belarusian and Ukrainian parts the Grand-Duchy of Lithuania used the system of principalities to occupy them by force or marriage (just changing the Great-Dich from Rurikid to Litthuanian). In that time a big remigration from the rich, but unstable Kievan regions to the safer northern regions around Novgorod can be observed, strengthening the eastern parts of the Rus that was to that point very peripheral.
In the end Moscow was the victor of the power-struggle for the title of the Grand Duke and with the diminishing power of the Khanat, was able to secure many principalities in the west (While the Ukrainian and Belarusian regions were under dispute for many centuries). Great-Duke Ivan the Terrible („the Terrible" can be more accurately translated with „the Awesome" in the sense of Awe inspiring) reorganized the system to a centralized autocracy and claimed for Moscow to be „the third Rome" after the destruction of Konstantinopel by the Ottomans. That reorganization in Tsardom brought with itself a disempowerment of Boyars, the nobles of that state we can call now Russia, and unlimited power for the Tsar, a real autocracy, that was uphold through sheer terror organized by the Oprichniki, the personal guard of the Tsar. The power of „might makes right" can not be overestimated until maybe the time of Katharina the Great who banned capital punishment, as punishments were draconian and militaries like the Oprichniki and similar organisations as the later cossacs roamed the country. Tsar Ivan also just started the Expansion to Siberia, so his Russia was big but not like Russia now. Also keep in mind that until the 20th century most Russians lived in small villages that were in no shape to resist even a strenuous, far away government, in the east were no rivals of government whatsoever until you came to the Chinese and maybe Mongolian border, and in the west the borders to Sweden, Poland-Lithuania and the Ottomans were often disputed and fought over with the help of cossacs and such.