There is no such thing as a "complete history" of anything, let alone all of humanity. A complete history would look like some sort of Borgesian experiment, a map of the kingdom on a one-to-one scale. A full accounting of humanity would be the size and scale of all of humanity itself.

There are some academics who do try to tackle history on that scale; some have pioneered an interdiscplinary "Big history". I, like many historians, look on this sort with something between real skepticism and detached amusement--these people are asking interesting questions, but they tend to ignore so much of what we've decided matters in academic history and often ask deeply ahistorical questions. Anthropologists often have their own, separate quibbles.

Instead, what you're looking for is global history or world history. I really like Adelman and Kotkin's World's Together, Worlds Apart. There are many others, including more basic high school textbooks. All of them sacrifice any kind of depth for breadth, though the best, like Adelman and Kotkin's work, also make big arguments.

However, I am especially leery of the idea of telling history, especially grand-scaled world history, through games. If you ask me, Civilization has done an enormous disservice to my generation's collective understanding of the past. So many people regard humanity as broken into a few, Huntington-esque, calcified civilizations. They definitely think that the 'evolution' of societies is linear and attendant on technology. It's like something from a 19th-century airmchair theorist.

You should be more precise, by what you mean. Because this could basically be everything.

I assume you're thinking of broader statements, and only the really big events. Like discovery of the New World by Columbus, discovery of electricity, discovery of gunpowder, etc.?

And probably also broad periods of development, like european medieval, roman empire, colonization, industrialization, feudal japan, chinese dynasties, etc.?