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Nobody was “proved to be correct”, because the winner of a poll does not by itself show anything about the probability of that particular candidate having won.
I think Nate's _interpretation_ was proved correct, and in the vein of "all models are wrong, some were useful," his proved useful (or would have if people were taking it more seriously) in both forecasting a more uncertain result as well as ancillary things like showing which states were"tipping point states" e.g. where should you put your money if you want to win.
Or rather, his interpretation was supported by the results, not proved
What does it mean to predict the probability of an event that can only possibly be tested once? Isn’t the prediction unfalsifiable?
Sure, if the forecaster and the model were only used one time.

But in 538's case they use the similar methods to forecast many individual contests like presidential primaries, presidential elections, senate elections, house elections, governor elections, club soccer, college football, March Madness men and women, MLB-NBA-NFL games and playoffs, etc.

Multiple-year track records over many events so you can compare their forecasts to actual results over time.

Get the data and compute your own error rate here: https://github.com/fivethirtyeight/checking-our-work-data

All of those things are very different though. It’s possible you could be excellent at predicting Senate races and terrible at the electoral college, right? And you only get one data point every 4 years.
There's a philosophical side to your question that I am not going to engage with, but for the practical you might be interested in this: https://en.m.wikipedia.org/wiki/Scoring_rule
The probability of winning is based on the popular support for a candidate. The poll directly measures that support. How can it possibly not 'show anything about the probability of that particular candidate having won'?
>The probability of winning is based on the popular support for a candidate

This isn't actually true. The probability of winning is based on aggregation of regional probabilities. The same national vote probability distribution can lead to very, very, different election probability distributions due to regional variation. The electoral college essentially guarantees that the national probability distribution is worthless for actually predicting who will be President.

Let's say we have two candidates A and B for some kind of election. We analyse our polling and other data, and estimate there is a 90% chance of candidate A winning and a 10% chance of candidate B winning.

If candidate B then wins, it does not mean that our analysis was "proved to be [in]correct". By itself, it doesn't actually say anything about the quality of our analysis. After all, we explicitly pointed out that this was a possibility, and it would be strange to argue "your analysis said this might happen, and then it did, so your analysis was incorrect". There's just not enough information to draw any conclusions.

It doesn't statistically. But if I say something has a 1 in a thousand chance of happening, and you say something has a 40% chance of happening and it happens... people will rightly say that your analysis was more correct than mine. Now maybe I was right and just got monumentally unlucky for unknowable factors. But that's certainly not the way people will think about it.
If one candidate won 1000 consecutive polls would it also tell you nothing about your estimate? This is obviously absurd: of course it would.

How about 100 times? 10 times? 2 times?

At what point does evidence cease to 'say anything about the quality of our analysis'? The answer is never. Every datapoint can be used to update your priors according to bayesian statistics.

As I said in my other comment that you chose to ignore, the probability of winning national popular vote does not indicate the probability of who will be President.
It's not that I chose to ignore you. I just didn't find your comment interesting from the statistical perspective.
You don't find aggregation of regional deviation to national deviation interesting from a statistical perspective? Odd.

Especially for someone who titles them-self "Chief Scientist"

I think you are right it can. But the last election is proof that the polls can fail to predict the outcome of an election.
Winning the election != winning the popular vote. There are plenty of qualitative reasons to believe the popular vote distribution matches the Economist model. He isn't arguing about how they came up with distribution. He is arguing that the particular kind of distribution is unreasonable in all instances. Which I disagree with. There are plenty of places in statistical modeling where a narrow head makes absolute sense.