Simply put (and ignoring the potential argument about whether or not the mongols are inflated), yes - the cultures that have more records (or were recorded by the more literate societies nearby) tend to have a greater chance at having a larger share of the "screen time" in our historical worldview.

This is because it's usually pretty hard to write about someone, or to accurately gauge their impact on global history when everything you know about them is from archeological data alone. It's sort of like the old saying "if a tree fell in the woods and no one was around to hear it, did it make a noise?"

I don't think anyone disputes that Eurocentrism exists in Western historiography. But I want to tread down a little different path here and make the argument that this is hardly surprising and, in some way, not unwarranted.

To use your Roman vs Mongol Empires premise I would argue that the Romans were far more significant to our daily lives than the Mongols. This is because the Romans built institutions and had a lasting impact on the places they touched - cultures which can trace descent from the Romans came to dominate the world during the Colonial era, thereby spreading many of their institutions and ideas to the Americas, Africa, and Oceania. Contrast this to the Mongols, who while an impressive people and Empire, left little lasting impact relative to the great span of their Empire. Probably as a symptom of their nomadic roots.

It's indisputable that the Western world was ascendant throughout the last several hundred years, and as such can be argued to be much more influential in the world than any other perspective. Like it or not, Western civilization owes a great deal to the Romans while I think Middle-Eastern, and Far-Eastern civilizations owe comparatively little to the Mongols.

So I guess I'm taking issue with the idea that we're 'inflating' or 'deflating' the importance of cultures, epochs, what have you. Eurocentrism is just a natural product of the significance the Western world has enjoyed for centuries.

That doesn't mean that the viewpoints and experiences of other peoples aren't important. It would be fascinating to have the perspectives of more native people in Africa or the Americas who were subjugated by Europeans but of course such accounts are few and far between.

But again, the prevalence of historical writings, in my view, points to the significance of a culture in their period of history.

I wouldn't discount geography and language. I can't say whether or not the volume of records has a large impact on modern significance of historical empires. But remember, the mere fact that we're both on reddit and are speaking English means that we are more closely culturally tied to the Roman Empire. Many people use it as a focal point in western culture. Maybe if we where living in Central Asia the conversation would be different.

There's actually a good deal written about the Mongols, though the early career of the empire's founder is less well-authenticated, and their place in world history is fairly prominent. But it's certainly true of regions which lack such records - most of sub-Saharan Africa and pre-Columbian America spring to mind, along with much of early south-east Asia.

In the west we're still struggling to get beyond a eurocentric tradition that formerly relegated even other great Eurasian subcontinents to the realm of sinology or indology. True world history is a fairly recent invention, but it's made great strides. But knowledge of less-documented areas will sadly always be limited by the scarcity of available records.

Foogers and Davepx both make good points. Another point to be made is that, to a certain extent, periods can be important historically because we have a large amount of historical records. For example, BC-era Greece had a much bigger impact on modern western culture than BC-era Germany because Romans, Renaissance Italians, Imperial-era Brits and so forth read ancient Greek legends and philosophy, but couldn't read BC-era German texts. If we had many ancient German texts and no ancient Greek texts, European culture would likely be somewhat different.