If it's not a good model, then you are welcome to pick it apart. However, the study that applied it for the 2017 paper in Scientific American found that it matches observed data about our economy stunningly well when applied.

As the author of that study was quoted here saying, the simple Yard Sale Model here can't begin to explain a complex economy, but its function is like an X-ray to cut through the complexity to see the bones of the thing.

In any case, we know empirically that Trickle Up is the actual effect of the capitalist system. If there's a model that can explain the mechanism more accurately, I'd be happy to hear it.

I think there is some confusion as to what this model represents. The linked article is not bad at explaining it but some things could be clearer.

First of all, the "money" in the model is not the cash you have at hand. It is the total value of all the things you own. This model does not need money and it also works if you exchange cigarettes for candy (as long as you can assign some worth to the objects).

It is also not about gambling. It assumes that every time you exchange goods with someone else, you can become richer or poorer (I like the example from the article: if you pay $200 for a watch that is worth $150, you lose $50, someone else gains $50).

It makes the extremely optimistic assumption that the chance to gain or lose money in a trade is equal. This is often obviously not the case in the real world. If you buy something from a supermarket, the owner wants to earn money, needs to pay their employees, needs to pay rent, ... so you know you pay more than the value of the goods you get.

Now this simplified and very optimistic model predicts that there is an exponential distribution of wealth and it predicts that repeated exchanges between a rich and a poor person will most likely result in the rich person getting richer and the poor person getting poorer.

What can we learn from that?
1.) even under these very optimistic conditions money trickles up. The real world is stacked much more against you, making a trickle down effect unlikely (though not impossible, this model is a simplification). 2.) rich people (in the model but imo it applies to the real world as well) are not smarter or otherwise better than the average person. They were lucky.
3.) Even if we remove a lot of the advantages rich people have in the world and construct a system that is seemingly "fair" (as in every one has the same chance) you still end up with super rich people. The only way to combat this is by redistributing money - tax the rich. Note that you still get an exponential distribution in the model but it becomes flatter.

What this model says nothing about is how the real world is stacked in favor of rich people. It tries to eliminate all these factors. So using this model to argue that inequality is built into the system (as the headline suggests) is somewhat strange. The model rather suggests that the inequality always arises from simple chance - One could maybe argue from it that we need to actively combat it (depends on the personal sense of justice if earnings due to luck should be redistributed).

I agree with you on the value creation. This model treats the economy as a zero-sum game. But the real economy is typically growing and this is ignored here.