One of these?

Well, that falls into the realm of chaos theory -- the notion that some systems are highly sensitive to initial conditions and that predicting the state of the system over time is impossible without perfect information about the initial state. Pop science reference point is "the butterfly effect". But I can't think of a snazzy, pithy word for that beyond that.

How 'bout autopoiesis?

The term autopoiesis was originally conceived as an attempt to characterize the nature of living systems.

Improbability?
Inevitability?

Fate, destiny. But maybe that's more deterministic than you want.

What you're thinking about is a counterfactual scenario. "If x had happened differently, then y would have happened differently as a result"

One way of understanding what we are talking about when we talk about counterfactuals is possible worlds theory. The idea is, when you make a counterfactual claim like "If Jeb Bush had run instead of GW, we'd all be wearing jaunty Speedoes now", your statement refers to another possible world in which Jeb really did run. And to see if your statement is true, we check to see what's true in that world.

Another term for the whole large scenario you're thinking about is an alternate history (that link covers what historians do with alt histories) and alternate history (that link covers what novelists do with them).

Oh, and you said you want the word for the humans there really are -- that would be the "actual world" in contrast to other "possible worlds".

Or, are you wanting a word for the amazing unlikelihood that the actual world would turn out exactly this way?

"anthropic principle" is one phrase to search for in connection with this, though it doesn't mean quite exactly what I think you're after.

Determinism! That's the field! From wikipedia:

"Determinism is the philosophical proposition that every event, including human cognition and behavior, decision and action, is causally determined by an unbroken chain of prior occurrences."

This is where I got tripped up in initially dismissing it:

"It is a popular misconception that determinism necessarily entails that humanity or individual humans have no influence on the future and its events (a position known as Fatalism)..."

The concept whose name I seek describes the current state as it is without regard for either free will or destiny. What do determinists call the present state, the "actual world", "hard reality"? Possibly the word I seek lies where determinism intersects existentialism.

Perhaps there is a legal term for this state: "you have no redress for the actions of past generations as perpetrated upon your ancestors, because without those occurrences happening exactly as they did, you would not be here today".

Obviously, you *had* to initially dismiss it, otherwise you would not have come to accept it. Everything happened as it should have happened. :-)

Anyone else read "causality" as "casualty" and be completely dumbfounded?
No?

As LobsterMitten says, the term you're looking for is "the actual world", which is one of those annoying technical terms that look more transparent than they are. But people other than determinists will also use that term to describe how things are (in contrast to how they might have been). Determinists believe that the actual world couldn't have been otherwise, and non-determinists believe that it could or might have.

Existentialists believe that "existence precedes essence", which can be tricky to explain but it is anyway a firm rejection of determinism. (You are you first and foremost; all those accidents of history are irrelevant). This makes for little room for intersections.

I suspect you are looking for a modern form of Stoicism, perhaps. You don't necessarily think that the way the world is, is the only way it could have been, but you see that you can't change things, so you should work out a way to accept them. One pretty good way to do this is to see that without the past being the way it is, you wouldn't have the present.

Not everyone would accept that though. Google "wrongful birth" for some examples.

But occhiblu's answer is much more Zen.