Traditional rationality goes back to Aristotle and is something that both Feynman and Popper rejected.

As others have said in the subcomments, this disputes the definition. We can have a debate about what should be called "traditional rationality", but it is not the discussion we are having now. The original post instead asked what "traditional rationality" precisely means in Yudkowsky's texts and what is wrong with that.

Popperian philosophy is not a set of rules

Does it mean that there are no rules in Popperianism? Can a Popperian scientist do whatever he wishes? (Yudkowsky's critique was that the rules of the traditional rationality - as defined by him - are rather insufficient, that TR allows one to hold much beliefs that Bayesianism rejects. So, even if it is the case that Popper = "anything goes", the critique would apply.)

In what sense does a probability correspond to an explanation?

In the sense that each explanation has associated a probability.

Lol.

Definitely not something you should include in your comment if you want your interlocutors to respond unemotionally.