Rationalism is the belief that reason is the primary path to knowledge, as opposed to, say, the observation that is championed by empiricism. It's a belief system that prioritises imposing its tenets on reality rather than asking reality what reality's tenets are. From the outset, it's inherently cult-like.
That is the definition of “rationalism” as proposed by philosophers like Descartes and Kant, but I don’t think that is an accurate representation of the type of “rationalism” this article describes.
This article describes “rationalism” as described in LessWrong and the sequences by Eliezer Yudkowsky. A good amount of it based on empirical findings from psychology behavior science. It’s called “rationalism” because it seeks to correct common reasoning heuristics that are purported to lead to incorrect reasoning, not in contrast to empiricism.
As an experience though, they could hardly have implemented it in a worse way. A big part of the reason I don't go to McDonald's any more is that the experience of using the ordering kiosks is so awful compared to just telling a human what I want.