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In my opinion, the most important feature of medieval Chinese life that the game should capture is the idea of a *career* in government. A successful character will move up the ranks, serve in various parts of the empire in different roles, and ultimately end up as a senior official at the imperial court. In the meantime they'll have set up at least one of their sons and/or nephews up for an official career of their own, and made some improvements to the family's private estate. This will be very different from the arc of a successful landed, feudal character, who wants to accumulate hereditary titles and pass those titles on to heirs. In short, the Chinese game would be very strongly skewed towards roleplaying and family management and away from the 'strategic' layer of land and warfare.
I think the best approach would be to do something like a balance between CK2's family palaces and I:R's holdings. Each, say, duchy capital (subject to balancing) is home to a number of Clan Estates. The Estates operate more or less like Palaces, being held by the playable clan patriarch and serving as a privately held source of income and prestige for when the clan members aren't in office. Giving a local/regional identity to each clan is historically accurate, and also helps get around the challenges with the limited number of Chinese surnames (i.e. the "Li clan of Henei" and the "Li clan of Longxi" is easier to distinguish than just an undifferentiated mass of unrelated people surnamed Li). If a family fails to produce any officials for a certain number of generations (subject to balance), then they vanish and a new clan is generated in their place, similar to what happens when a patrician family falls.
Officialdom offers several different tracks. The largest is the civil administration, meaning the landed titles. Second largest is the military (military officials operate something like CK3's bishops, taking in all the levies/men-at-arms for a particular region/ de jure title without holding all of the land and tax base, which remains in civil administrator hands). A third, open mostly to women and eunuchs, is through the imperial household- a path which is not particularly prestigious and can be very dangerous, but which may lead to the fastest access to the Emperor and his circle. A successful clan will likely produce many civil officials, including some members of the imperial court, as well as the odd military official and numerous concubines or consorts to the Emperor and his clansmen. Or, a player could specialize in one particular path, whether their goal is to influence the Empire or to usurp it. Different stats should all influence a character's ability to succeed in these tracks, but in very different ways. Characters can rise through competence, effective networking, corruption, blackmail or a variety of other methods.
One important aspect of this would be to divide up the 'authority' of assigning positions/titles. The Emperor should not be able to appoint, investiture-style, every civil administrator from the county on up. Whether through decisions, events, or otherwise, no single individual in the Empire should have total control over a system as vast, complex and inscrutable as the Chinese imperial bureaucracy. It needs an element of opacity and unpredictability.
Another is the examination system. Under the Tang, most officials came from the great families and only a minority passed through examinations, but in the Song the examination system became universal and the power of the great clans receded. Sitting for the exams was an important milestone in the life of a young man of the gentry, and performance on them greatly impacted their career prospects and prestige. But it was also a fact that graduates often greatly outnumbered actual vacancies, so many educated members of the gentry class lived private lives on their estates as artists, scholars, and local leaders- meaning there is plenty to do even for those members of the clan who are not holding a position in government. A son or nephew who fails to gain office, but who produces a major artistic or literary work, can still enhance the family's prestige and benefit his kinsmen.
All of this is relevant for the normal, playable clans under the Chinese empire, but for the imperial line things will be a little bit different. Although the Emperor doesn't have direct and total control over the running of his realm, being forced to rely on the professional bureaucrats and officers under him, he is very concerned with the defense of the Empire and the stability of his clan's hold on the throne. A Mandate mechanic (based very, very roughly off of Decadence) represents the imperial clan's right to rule, and is increased by effective governance, victory in war, economic prosperity and good omens, but threatened by corruption, inefficiency, defeat and natural disasters. Many of the choices pursued by individual characters and clans in their own self-interest are damaging to the Mandate in the long run, so the Emperor is burdened with seeking out sources of the erosion of his Mandate or offsetting them with successes on other fronts. And at the same time that elevating capable officials is good for the realm, it can also put those same people in a position to usurp the throne.
In short, to make China playable you'd need to greatly flesh out the domestic politics, interpersonal relationships, day-to-day events and civil-military divide, aside from making some tweaks to how government works in game. But I think that these changes would make Chinese gameplay into a really unique and enjoyable experience, while also offering improvements to other regions (ERE in particular, but potentially any centralizing late-game realm).
