I don't think there's a single defining point of difference, but I tend to think of it as the difference between the traditional social standard of having beliefs you can defend and the stricter individual standard of trying to believe as accurately as possible.

The How to Have a Rational Discussion flowchart is a great example of the former: the question addressed there is whether you are playing by the rules of the game. If you are playing by the rules and can defend your beliefs, great, you're OK! This is how we are built to reason.

X-rationality emphasizes having accurate beliefs over having defensible beliefs. If you fail to achieve a correct answer, it is futile to protest that you acted with propriety. Instead of asking "does this evidence allow me to keep my belief or oblige me to give it up?", it asks "what is the correct level of confidence for me to have in this idea given this new evidence?"

Eliezer uses "Traditional Rationality" to mean something like "Rationality, as practised by scientists everywhere, especially the ones who read Feynman and Popper". It refers to the rules that scientists follow.

A surely incomplete list of deficiencies:

• The practitioners only use it within some small domain.
• Maybe they even believe that one can only be rational in this domain.
• Designed to work for groups, not for individuals. Telling someone to use Science to become smart is like telling them to use Capitalism to become rich.
• It doesn't tell you how to create hypotheses, only how to test them.
• Imprecise understanding of probability and knowledge (which are the same thing).
• Bizarre fetishisation of "falsification".
• Failure to concentrate on the important problems.

In some ways, Eliezer is too hard on Traditional Rationalists (TRists). In the "wild and reckless youth" essay, which you cite, he focuses on how TR didn't keep him from privileging a hypothesis and wasting years of his life on it.

But TR, as represented by people like Sagan and Feynman, does enjoin you to believe things only on the basis of good evidence. Eliezer makes it sound like you can believe whatever crazy hypothesis you want, as long as it's naturalistic and in-principle-falsifiable, and as long as you don't expect others to be convinced until you deliver good evidence. But there are plenty of TRists who would say that you ought not to be convinced yourself until your evidence is strong.

However, Eliezer still makes a very good point. This injunction doesn't get you very far if you don't know the right way to evaluate evidence as "strong", or if you don't have a systematic method for synthesizing all the different evidences to arrive at your conclusion. This is where TR falls down. It gives you an injunction, but it leaves too much of the details of how to fulfill the injunction up to gut instinct. So, Eliezer will be contributing something very valuable with his book.

Plus, the focus in TR on whether you ought to be convinced makes it seem like belief is binary. Under TR, you're always asking yourself, "Is there enough evidence yet so that we ought to be convinced?" TRists will talk about probabilities and error bars, but there is an incomplete acknowledgement of the fact that you ought not to think in terms of thresholds of belief at all.

I just started listening to THIS (perhaps 15min of it on my drive to work this morning), and EY has already mentioned a little about traditional rationality vs. where he is now with respect to reading Feynman. I'm not sure if he'll talk more about this, but Luke's page does have as a bullet point of the things covered:

Eliezer’s journey from ‘traditional rationality’ to ‘technical rationality’

so perhaps he'll continue in detail about this. Off hand, all I can specifically remember is that at one point he encountered some who thought that multiple routes to solve a problem might lead to different, but correct, answers. Then he read Jaynes, who said that this was all wrong -- all mathematically valid routes to real solution should and will converge.

Also, there's a whole series of posts on EY's "Coming of Age" HERE, but maybe you knew that and still aren't satisfied.

One relevant attempt at a definition:

I will be using "extreme rationality" or "x-rationality" in the sense of "techniques and theories from Overcoming Bias, Less Wrong, or similar deliberate formal rationality study programs, above and beyond the standard level of rationality possessed by an intelligent science-literate person without formal rationalist training."