America is indeed a relatively young nation. However, depending on how look at it... it isn't the youngest. In a literal definition Germany is younger, albeit also represents pre-unification Germany too (particuarly Prussia).
However consider the follow. Indeed America has a profound effect on the world in many ways: culture, politics, etc. I won't say the US "saved the world" in WWII, however America developed the A-bomb (even if it was inevitable, they did it)... without the USA the war would certainly have been dramaticly different (if you include US Industrial, and Economic assistance). Just look at the Cold War. America and Russia were the primary drive in *global* politics for 60+ years, and America still does. During the Cold War most countries sided with the USA in debates in the UN. Also as people have pointed out American culture (tv, movies, and even literature) is to be found around the world. Music (and music styles) as well.
In less then 200 years America went from a near back-water country to a super-power on Earth (not a region). Not exactly a normal thing for a civ/country. The USA has had a profound impact on the entire planet, both in the past, present, and future. Few countries have had that level of impact, let alone in such a short amount of time. When the USA speaks, the world does listen. Not out of fear, one could point to a number of countries that should've feared the US and didn't cooperate. Most countries listen as they have far more to gain by working with America, on many levels. Sure you could claim America is arrogant, but one could not say that's always the case. Most countries do have a level of arrogance, and America also likes to cooperate as it often has more to gain from doing so.
Also not everyone has respect for the US becuase of the 'or else' aspect. America has done a lot of good things, and not everyone likes admitting that. Even Americans don't like admitting other countries have done good things for them. Many informed people will look at many nations, respect them, but feel free to call them on thier faults. Indeed, many patriotic Americans will aknowledge its faults (past or present), but still love thier country. I'm very conservative, and I don't see America as "perfect", and I love my country. I base my view that America should be in Civ not because I live here or my love for it alone, but on a historical context. I'd also defend other civs left out (ones that have been in civ or ones I think should be in), as I consider them significant. Indeed I may very much respect this country, even if I realize they are imperfect and may have done things in thier history which are objectionable.
As for the comments about "american cultures" there is debate about what multiculturalism is, is there more then one kind, etc. However, if you look at civics and social studies textbooks in the US (past and present) being American isn't a race, ethnicity, faith, etc. It's more of a way of thinking. Look at other countries. One could take, let's say France or China, and divide it up into subcultures if one wanted, however the people of those countries don't concern themselves with those identities even if they are aware of them. Americans see themselves as that, Americans... sure there are differences, we accept this and even appreciate that, although look at our history. When times get tough, we value the things we share in common... and indeed we have many things in common. Are there exceptions? Sure. Bigots? Sure. They exist in every culture/group/etc. However what about as a general concept? Then you see it.
Sure, we have a troubled history... but that's because we're *human*. What you do notice is a general trend forward to get away from that and put it behind us. A progressive attitude. While this certainly isn't unique here, I think it balances things out. Heck, the progressive attitude is something to feel good about (even though one may feel bad it was needed).
Other arguements do stand, America has made many accomplisments other countries have not... and many more still few achieve. We've gone to the moon, and only Russia has ever attempted to aside from us. I think China is looking at doing it. America is the only country to have sent probes into deep space. Voyager I, launched in 1977 is STILL sending signals and should until 2020.
http://en.wikipedia.org/wiki/Voyager_I If you want verification. America does has a history of inovation. Granted, these modern evaluations don't help the ancient civs... but several civs exist today (both in the game) and 100s of countries today... and only a handful of today's (2-5) could be represented... represented as in due to reasons of the last century... then the USA is at the top of the list with Russian, Germany, and China close behind... although China deserves to be in due to reasons across several millenia (which being millenia is a reason in of itself).
Saying countries didn't exist back then is hardly a fair arguement. Until they create a mechanism for civs to grow out of old ones, etc... then I think that arguement is invalid. Even Rome and Greece would likely be excluded then.
Back to the cultures arguement... have you considered that might be the American culture itself? This can be taken more then one way of course. Elements of each culture adding up to the total American identity, the melting pot analogy, etc are all something you associate with the USA (if not always the other way around). If I wanted to, I could discuss each Civ in detail and discuss how it's not really one specific culture, but has mutliple cultures within it... past and present. I could discuss how each civ merits being in, and I'd say America would be in the top 20 at least... certainly not top 5.... but more then worthy of being in Civilization and even worthy of being in the initial release of such a game.
WIth as "short" a history the US has had, and had this level of impact? I think that speaks in of itself.
Besides: An American did create this game.
EVERYONE who plays this game has been affected by America in that way (and likely what they play it on)
Although Linux (IIRC) is Swedish.
Computers are primarily due to the US. Sorry, it's true... but somewhat humerous to end my post on a more positive note.