I realize the spirit of the OP was that of which civs have already "won" and by what condition(s). But I thought it would be interesting to examine each VC in turn. I don't know how to define the parameters of a "civilization" vs. the more ephemeral dynamics of a "nation", so grains of salt disclaimers probably apply
Time: This might be the only condition where existing civilizations could apply if a given duration was provided. Two obvious regions based on reliable age estimates are the Mesopotamian and Indus valleys. But the nations of Iraq (Mesopotamia), Afghanistan and Pakistan (Indus) are very new geopolitical constructs and remain under assault. While some culture may remain intact, waves of militaries and religions have redefined these areas and their resident cultures. That would probably leave us with India as the oldest, most coherent civilization that remains viable to this day.
I don't know how colonial rule or outright invasion would affect the calculation, however. India only recently reclaimed its sovereignty from the British empire. Likewise China from Japan. And then there's Egypt whose true age is anyone's guess.
Science: Let's assume this condition would be satisfied by a successful colonization of a planet in another star system (e.g., Alpha Centauri) or by technology so advanced as to make the very idea of civilization -- or even individual identity -- essentially meaningless. It's highly unlikely that this would be accomplished by any one nation, nor would it carry with it the same arbitrary political significance.
I view interstellar travel as a barrier of entry for budding civilizations of intelligent lifeforms. It's perhaps fortunate that the distances involved require the same technological progress that could also be used to end (or significantly set back) civilizations who are not yet ready for galactic-level citizenship. When (if?) humans are ready, I don't think we'll be waving flags of nations or corporations. We'll need to evolve psychologically and sociologically such that these fixations no longer serve as such lethal obstructions.
I've not played Civ:BE, but I can speculate on one of its affinities. I believe that terrestrial evolution is following a progression from random mutation (asexual; cloning) > natural selection (sex and death) > artificial selection (forced / manipulated breeding of traits) > genetic engineering (creation / manipulation of traits and organisms) > cybernetics (approaching real-time adaptation to environment which once would have taken generations through previous evolutionary means) > ??? (perhaps no biological, or ultimately, no physical form at all)
I sense that life will eventually fully transcend its biological origin and ensuing limitations. I assume its worldview would be entirely alien and inaccessible to us. I suppose its victory would be enlightenment -- or the realization that it is literally the consciousness of the Cosmos as it becomes self aware. I digress.
Domination: This VC seems the least plausible and the least interesting to me regardless of technological era. To satisfy its requirements, the capital (or equivalent seat of power) of each coexisting civilization would need to be captured and controlled at some point (not necessarily at the same time?) by a single civilization. I also suppose this would apply even if the conquering civ were allied or otherwise participating in a coalition. Germany and Japan made formidable advances on a global scale, and had they access to nuclear technology at the time . . .
Cultural: This one is impossible to quantify. Culture is an evolving dynamic -- not a collection of static relics in a museum. Insular societies may have preserved and sheltered their culture for longer than others. I'm thinking classically of Japan, but more recently maybe of Iran or North Korea? Or perhaps the Great Firewall of China trying to filter and control access to information from something as boundless as the Internet? Nothing seems impermeable to cultural pressure and influence.
The issue I have with this VC is that no culture exists in a vacuum unique to itself. America is famously the "melting pot" of cultures, and ultimately, the Earth will be as well. Eventually, any distinct qualities of race, ethnicity, and "culture" will homogenize. There will always remain (and newly evolve) regional characteristics, but as time goes on, they will become much less fundamentally distinct. Monoculture FTcvW??
Diplomatic: I would like to think that such a victory could be achieved through mutually beneficial diplomacy, but instead, I fear it's the proxy for the "true" domination victory. Global hegemony. It'll be achieved primarily through the consolidation of economic control, and could be a runaway phenomenon that dictates all other aspects of civilization. Even though nations participate with varying degrees of diminishing autonomy, this victory will be awarded to the multinational global elite who have basically usurped governments to legislate (and enforce militarily and through espionage) on their behalf.
This is the classic struggle that humans have faced since we began trying to civilize ourselves. In CiV, we're presented with three overriding ideologies: Freedom, Order, and Autocracy. Which translate to Capitalism, Communism, and Fascism. It seems that there are barely just two competing ideologies today -- capitalism and vanishing communism. Either social order can descend into authoritarianism, and we've seen it happen. While capitalism might market itself with the banner of freedom, it's indistinguishable from fascism if taken to its nth degree. A truly just and egalitarian society remains a noble goal, but one which we've never seen on any significant scale. That, IMO, would be the only real victory for civilization itself, and the one aspiration any otherwise fledgling civ should be aiming for.