This notion that the world, or humanity at large, might be fallen from some earlier "perfect" state is of course found all over the place in the history of thought. By way of example, a description of the Golden Age, or the age of Truth, from the Mahabharata:
> Men neither bought nor sold; there were no poor and no rich; there was no need to labour, because all that men required was obtained by the power of will; the chief virtue was the abandonment of all worldly desires. The Krita Yuga was without disease; there was no lessening with the years; there was no hatred or vanity, or evil thought whatsoever; no sorrow, no fear. All mankind could attain to supreme blessedness.
(There might even be something to it, given how long human history from the emergence of behaviorally-modern humans (10,000 BC?) to the beginning of the historical record actually was. Who's to say that human societies in that time period did not gradually evolve to a sort of cultural- and value- "modernity", that was subsequently forgotten in some sort of great, worldwide social crisis? That might have been the true "Fall from Eden" perhaps, scattering human societies far and wide.)
Yes, Scott's essay and the Christian idea of fallen-ness both fit the following high-level description: "The world is in a mess because of the way people are."
No, they are not the same idea, and claiming that they are (1) is unfair to Scott, since it suggests that all he did was to take an idea that "we" (i.e., Christians) already had and express it well; and (2) promotes Christianity in a way it doesn't deserve, since it suggests that Scott's specific and ingenious account of just how human nature leads to the world being a mess is one that "we" already had.
For all I know, perhaps some individual Christian thinkers had the same specific insights as Scott -- e.g., I think C S Lewis had some smart things to say about how the essence of hell is competition, or something like that -- but it certainly isn't accurate to say that "we" mean what Scott describes.
[Disclaimer: I am not a Christian. But I was one for multiple decades. When I say "we" above I am echoing NateEag's language.]
1. Christian ideas of "fallenness" do not generally involve Scott's insights about game theory and coordination problems.
2. Christian ideas of "fallenness" generally emphasize other aspects of human sinfulness besides the ones relevant to Scott's analysis (selfishness, greed, competitiveness).
3. Christian ideas of "fallenness" generally incorporate (as important features) elements that are conspicuously absent from Scott's analysis. "Cursed is the ground because of you": following Genesis, Christians commonly reckon that the world's "fallenness" explains its imperfect hospitability to human flourishing: just as some people look forward to a "post-scarcity" society, the Garden of Eden (whether regarded as historical or mythical or both) is a "pre-scarcity" society: one that provides everyone with what they need and want. "Since death came by a man, so the resurrection of the dead also comes by a man.": following 1 Corinthians, Christians commonly reckon that the very existence of death is the result of human "fallenness". None of this stuff is in Scott's discussion of Moloch; none of it needs to be.
(To keep myself honest, I just did a little experiment: I looked up Genesis 3 and 1 Corinthians 15 in a few books I had on my shelf: the "New Jerome Biblical Commentary" (one volume, liberal-ish RC), "The theology of the book of Genesis" by R W L Moberly (Anglican), the "Cambridge Bible Commentary" on 1,2 Corinthians (liberal Anglican-ish). I also looked up "fall" in the Oxford Companion to the Bible (liberal-ish Anglican-ish) and the "Concise Dictionary of Theology" of O'Collins and Farrugia (middle-of-the-road RC), which are the only two encyclopaedia-like things I have handy. There's no hint in any of them of anything like Scott's analysis. Of course that's a small sample, from a narrow-ish range of theological perspectives -- no evangelicals, traditionalist RCs, Eastern Orthodox, death-of-God ultraliberals, etc. -- but I think it's enough to make it clear that it's not true that Scott's analysis is what "we" (= Christians) mean by the idea that the world is fallen.)
You're misunderstanding the entire point of Christianity, in the interest, perhaps, of a snarky quote? In Christianity, the world will always be fallen, sure. The whole point is that it is. The non-fallen place is heaven- that's where "our diety" is: bringing those who'd actually want to be there to Heaven. What we do in the meantime is try to make the world as less-bad as possible.
For the world being fallen:
"Therefore, just as sin came into the world through one man, and death through sin, and so death spread to all men because all sinned." (Romans 5:12)
"Cursed is the ground because of you; in toil you shall eat of it all the days of your life; thorns and thistles it shall bring forth for you; and you shall eat the plants of the field. By the sweat of your face you shall eat bread until you return to the ground..." (Genesis 3:17b-19a)
Our mission on Earth:
https://bible.knowing-jesus.com/topics/Charity
Note that most of these quotes are very often used (and quotes here) in such a way that it wouldn't even be sustainable to survive and continue giving. You have to use your brain, even with Biblical commands, in order to carry them out it seems.
Take note here that I don't even think any of this is necessarily moral or a good idea. But it's easy to find!
> Men neither bought nor sold; there were no poor and no rich; there was no need to labour, because all that men required was obtained by the power of will; the chief virtue was the abandonment of all worldly desires. The Krita Yuga was without disease; there was no lessening with the years; there was no hatred or vanity, or evil thought whatsoever; no sorrow, no fear. All mankind could attain to supreme blessedness.
(There might even be something to it, given how long human history from the emergence of behaviorally-modern humans (10,000 BC?) to the beginning of the historical record actually was. Who's to say that human societies in that time period did not gradually evolve to a sort of cultural- and value- "modernity", that was subsequently forgotten in some sort of great, worldwide social crisis? That might have been the true "Fall from Eden" perhaps, scattering human societies far and wide.)