I think our core disagreement is that I do not consider teaching falsehoods to be educational. My antipathy towards LLM outputs that haven't been fact-checked is mostly downstream of things like that.
I think most players would understand that in-game choices will not reflect the choices people actually made historically. Having not played Civilization, I'm not sure whether I would consider it to be educational -- I think it would depend on whether playing the game provides insight into real historical events.
For example, I would consider a sufficiently detailed LARP of a historical event to be educational[1] -- the actual choices and outcomes do not match what happened historically, but they can teach participants a great deal about the motives and limitations of real historical actors.
This website, on the other hand, seems to consist of 90% AI hallucinations and 10% data that was actually extracted from a real source[2]. Since these types of data are thoroughly mixed together, I think this website is about as educational as just making up something to believe about the past.
[1] https://college.uchicago.edu/news/academic-stories/history-c...