Why didn't other cultures write down their history to the extent that Europeans did?
You just asked a very similar question 21 hours ago. Is there any particular question you are reasking it, as in, do you have an answer you want? To quote my answer there:
Why do you think this is the case?
For example, the Court Diaries existed in some form, on and off, for nearly two thousand years until the very end of imperial China (with precedents going back almost three thousand years): to quote Chinese History: A Manual, they "recorded the decisions and actions of the emperor in the conduct of government business, normally as this occurred in formal sessions of the imperial court each morning." While most Diaries from earlier periods no longer survive, the Court Diaries for the Qing Dynasty do. The Qing Court Diaries begin in 1629, were regularized in 1670, and continued to be written up to 1911. Not even the emperor himself was privy to them. Some 12000 volumes were written: they are still not fully published simply because of the sheer size of the archives.
The Court Diaries were not the only daily records of the Chinese government. We also have the Records of Current Government and the Daily Calendars (the latter being a condensation of the Court Diaries and the Records of Current Government). Nor were these forms of annalistic history limited to China. For example, the Daily Calendars of the Royal Secretariat, written by royal secretariats of the Joseon Dynasty (1392~ 1910) of Korea, include 3245 volumes, despite the first 231 years' worth of Calendars being lost due to various wars and rebellions; the 3000+ surviving volumes comprise of 230 million characters (note that a Classical Chinese word is a few characters at most and frequently just one character).
From these sources were published the Veritable Records of East Asia, which are less detailed but more organized. Most Chinese Veritable Records before 1368 are lost, with only a small fragment from 805 and a longer fragment from 983 to 996, but the Ming Veritable Records are completely intact and its 2909 volumes are the single most comprehensive source for the dynasty. The trilingual Qing Veritable Records are even longer (about 30% more than the Ming Veritable Records). Going back to Korea, the Joseon Veritable Records are composed of 1893 volumes; in Vietnam the Dai Nam Veritable Records have 584 volumes despite covering less than two centuries.
In Chinese thought, history was so important that each dynasty had a duty to publish a history of its predecessor. The Mongols would write histories of the Jurchens and Khitans and Chinese, the Ming would write histories of the Mongols, and the Manchus would write accounts of the Ming.
Overall, we have 200 different kinds of governmental histories and records from the Ming Dynasty alone. Then there are many many more private histories, which often portray a different perspective from the government standard (ie Unofficial History of the Rise of the Ming).
TL;DR This isn't really the case