What do they get right/wrong, what narratives and myths do they perpetuate, how do you feel about how they use history as a setting for grand strategy?
So I have played Crusader Kings II and III and Europa Universalis IV since these overlap with my periods of interest. Overall, I like the series and what Paradox has done to encourage people to become interested in history.
My biggest complaint is that these games are too static when it comes to ideas of nations/territory and often 'lock' history into particular paths.
In both CK and EU, the basic units of territory are static. In the past, boundaries of counties (if they used that term) varied over time. In the world I study (Iberian history) such jurisdictional boundaries were constantly being disputed by different communities and nobles. They certainly were not static and they were not even commonly recognized. Second, and related to that, the idea of specific de jure higher level groupings of those base units is quite ahistorical. Using Spain as the example, sure by the 15th c. there was some sense that Christian kingdoms SHOULD regain the territories still controlled by Muslim rulers, but there was certainly no sense that Castile and Aragon SHOULD become united.
You could add the notion of culture to this. Cultures change evolve over time. Yet, in these games it is static. In reality, cultures split evolve, converge, adapt. Again, England or Spain are good examples. Saxon, Angle, Welsh, Irish, Dane, Castilian, Aragonese, Portuguese were never static concepts in some cases they shared a common cultural origin in others they converged over time as conquests and expansions interspersed their members.
For a further example, Castile and Aragon were not actually united under Ferdinand and Isabel, nor their Habsburg descendants. There was a dynastic union in which the kingdoms were ruled by the same person but they were autonomous political entities with entirely distinct political organizations and institutions (the same was true of Portugal during its union to the Habsburg monarchs, 1580-1640). There really was no political entity for 'Spain' until at least the early 18th c. and the reorganization that followed the rise of the Bourbon monarchy.
For a similar example, just jump up to England. There was no universal sense of a united England, sure it became a goal of the monarchs of Wessex, but it was not a 'de jure' entity. It was an ideal that eventually was achieved. It gained salience after that union, but not before.
So the crux of my complaint here is that these games tend to engage in a post hoc ergo propter hoc fallacy, because it was after therefore it was before.
One of the most interesting parts of history is understanding the contingent and contextual reasons why things come to pass. These games assume a particular outcome and then use that outcome to establish particular rules.
Related to that is the way that certain outcomes become goals (this is especially true for EU and I believe later games like Victoria) where historical events that were contingent on many factors become goals that can/should be achieved.
I get why it might be fun to try and achieve these particular events (unification of kingdoms, revolutions, etc. ) before their actual historical period, but the fun of these games, at least for me, is engaging in counterfactual history. Yet, it is hard to engage in counterfactual history when the game privileges the actual past in the logic of the game.
If these are the people who make whatever the hell game that is where you have to unify "Jianzhou," "Haixi" and "Yeren" in order to form "Manchu," I would caution that those first three terms are categories of Ming imperial foreign policy. Tinkering a bit with Yuan precedent, the Ming Empire decided that the peoples of the northeast were "Jurchens," and slotted them into various "types" in an application of age-old strategies aimed at attempting to keep the barbarians divided.
The three big names were chosen with no reference to terminology used by the peoples of the northeast or to any 'indigenous' conception of 'self-identity.' All three are Chinese words. Haixi and, probably, Jianzhou are geographic concepts: 建州/Jianzhou appears to be a proper name, but neither the specific location of a place that could have been Jianzhou, nor the origin of the term itself, is agreed upon. 海西/Haixi literally means "west of the sea" which is kinda difficult to rationalize at face value (the entirety of Manchuria is west of the sea). I've seen attempts to claim that 'Haixi' involved an early name/alternative reference to the Sungari/Songhua river, and the tribes that 'Haixi' is usually understood to cover were indeed based on the west side of the upper Sungari (most of my sources would be in Chinese).
野人/Yeren means 'savages,' or literally: 'wildmen.' Again, this clearly wasn't a term that the supposed Jurchens in supposed question here were using amongst themselves. There are longstanding debates over the origin and meaning of the various words translated into English as 'Jurchen,' often emphasizing the apparently negative connotations. 'Jurchen' could be coming from a Khitan word for 'slave;' in Manchu, 'juxen' can still refer to 'servants/underlings,' often in the sense of 'subject peoples' (there is an absolute pile of scholarship looking at the Aisin Khanate/early Qing's variously shifting attitudes towards the use of the term 'juxen'). 'Yeren,' on the other hand, is point-blank insulting. So much so that secondary literature here in the PRC no longer uses this word- in the interests of upholding the Party's line of 'unity among the peoples,' we've anachronistically replaced 'Yeren' with 东海女真/Donghai Nüzhen 'the Jurchens of the eastern sea.' Outside of this, we take the same Sinocentric approach to Manchurian history that this game does- it's just this one term that's different.
There are, of course, records of a guy like Nurgaci presenting himself to some representative of Ming officialdom as "whatever title he had that day" of "the Jianzhou Left Guard" or whatever. This is simply how anything got done with the central plains-based empires of the south. The go-to here is Thomas J. Barfield's The Perilous Frontier: Nomadic Empires and China, 221 BC to AD 1757 which offers a history of how the Central Eurasian peoples learned that it was much easier to play along with the decorum and whatnot of the Han or Ming Empire's version of reality than to raid the borderlands whenever times on the steppe were tough. An international trade racket-slash-ginseng cartel of the type Nurgaci was running early in his career could also organize and support infinitely more people than a loose tribal confederacy thrown together by a charismatic leader's intermittent ability to distribute pillaged booty. The main condition for winning access to resources unavailable back home- without fighting too much for it- was having to pretend that 'Jianzhou' was a thing and that the emperor in his magnanimity was letting you rule it. Quick note that Barfield's book was published in 1989 and many of its specific positions have been superseded since then. A big name in this regard is Nicola di Cosmo, who starts off from Barfield, but whose research imparts considerably more agency to the northern peoples than Barfield was able to allow given the relatively limited sources at his disposal.
There's a discussion of a map here that gives an idea of what this game's 'pre-Manchu' regions look like when we move away from the received, Sinocentric ideology and instead turn to contemporary Manchu-language sources. The map itself was made way after the fact and is rather idealized, but gives a good selection of the terminology used by the Aisin Khanate/early Qing when discussing "its own" history. In the various yargiyan kooli/实录 "Veritable Records" of the reigns of the early Aisin/Qing rulers (as in, the texts where these names are coming from), there is no mention of concepts like Jianzhou, Haixi, or Yeren, much less Donghai.
English-language readings on the early empire:
Pamela Kyle Crossley, The Manchus. Blackwell Publishers, 1997
Gertraude Roth, "The Manchu-Chinese Relationship, 1618-1636," in Spence and Wills, Jr, eds., From Ming to Ch'ing: Conquest, Region, and Continuity in Seventeenth-Century China. Yale University Press, 1979. There's also her chapter (as Gertraude Roth-Li) "State Building Before 1644" in The Cambridge History of China, Volume 9, Part 1: The Ch'ing Empire to 1800. I've never gotten my hands on her doctoral thesis but would absolutely love to read it.
While we're here, the idea that the Qing Empire had a "flag" is pretty iffy, but that's a discussion for another comment. Also, this is supposed to say 'aisin gurun' meaning 'the Aisin (gold) Khanate/state/tribe/etc.' Getting technical here, it's ugly af. It's hard to say what's going on with the r and second u in 'gurun,' and while the ai- initial in 'aisin' isn't 'wrong,' you'd also rather not write the 'i' like that.
Edit: apologies for attitude... Literally just last night I read a paper in a respectable journal published by a very respectable UK university where the author (a PhD student) made the claim (in a footnote) that the ilan hala/三姓 "three tribes" or "three surnames" mentioned in the very earliest Taizong versions of the Manchu foundation myth may be a reference to the Jianzhou, Haixi and Yeren. I have zero clue as to how that made it past the editorial staff.
There's always more that can be said, but while you wait you might want to check out the Crusader Kings III/Medieval Period Flair Panel AMA: Come Ask Your Questions on Incest, Heresies and Video Game History!, featuring a variety of answers to specific questions about that game and time period from users such as /u/Rittermeister, /u/WelfOnTheShelf, and /u/sunagainstgold among many others.