Europe (or the "West" if we want to include European descended nations like the US), has been the hegemonic power that has largely imposed its system of institutions and certain "universal" beliefs during the last few centuries (some of which existing prior to the European world-system in various cases). The nation state and the equality of nation-states, national education systems, equality of man and of woman, the market economy, the secular state, human rights, democracy, even our concepts of race and class etc. etc.; such are things that while not really "universal" in that not every country has them because there are many countries which don't, are still "universal" in that the sense that they are the hegemonic model and form the baseline for how peoples should be organized. Of course, these vary to greater and lesser degrees; nobody gets away without a version of the nation-state, with absolute and formally sovereign borders even if internal make up may vary, while democracy can be let slide, even if its still the assumed preferred model.
But, what if Europe and its descendants weren't the hegemony? Generally the power which is assumed as the competitor to Europe that could have fulfilled the same role is China, but it could be anyone, provided its able to achieve the same dominant position in the world that the European system was, imposing that upon the rest of the world. How much do you think that they would have the same "universal values" if they're the ones who form the nexus of the world system? Do you think that many of the above values stem principally from the European intellectual heritage, or instead that they're an inevitable progress of the systems that would accompany the move to a "modernity" such as the spread of literacy and economic development, even if it isn't a Western modernity? For that matter, what might be alternate "universal" values and institutions, that might develop if it was China or India that took Europe's place?
From my personal viewpoints I think that a lot of the elements spread by the European world-system might arise elsewhere, as a product of social-material conditions which I can't imagine can be too different in an alternate modernization (as an example, it seems inevitable that mass literacy is going to accompany it regardless of who carries it out, and in my opinion that makes nationalism inevitable, and nationalism seems like it would pave the way for a lot of the after mentioned values/institutions such as the horizontally organized and egalitarian citizen body), but I'm sure there would be plenty of differences as well.