The way I understand it, there is only rational thinking and thinking with no grounding in reality whatsoever- i.e. making things up or emotivism which comes to the same thing. Since you clearly have some other means, I assumed I didn't understand you.
The way you understand it is quite inaccurate. I'm not sure whether this is your issue with your understanding of rationalism, but: one of the big problems with the clause "rational" is that it has become a great 'pop' word if you want your points to sound smart. Therefore it's often misused in journalism and politics as an empty plusword without actual philosophical meaning. ("This policy is rational, therefore it is good" "You are irrational, therefore I'm right") It's often nonsense, being a synonyme to 'good', leading, at times, to embarassing truisms. For this debate I really couldn't care less about stupid monickers the media borrow from philosophy to make-pretend, but within a philosophical discourse you have to use philosophical tools, not pluswords.
Rational thinking binds itself to the mind, to logic, to syllogisms. To ration. Not to the world, actually, not as it shows itself to us; rational thought can be done independent of experience. Mathematics is a rationalist tool, for example. It has no grounding in reality whatsoever, but is used to parse reality. Same with logic and your cruel demon guy. What you provide is a critique of rational objectivity. Not an
experience of truth which to some philosophies is all that is relevant. Denouncing all philosophical methods on the grounds of one is a kinda bad thing.
There are plenty of thought structures and argumentative methods that exist beyond rationalism. Science, for example, while prevalently borrowing from rationalist constructs, relies heavily on positivism in order to function at all, which is an empirist reality model. There's of course also the often disdained emotion, which you yourself denied upfront in your premise, which is really sad. Emotion is a big part of being. I myself like phenomenology and that method of thinking does not concern itself with monolithic truths, but rather morphological structures that can be approximated but never really known.
A simplistic (and shorter) reply could be that traditionally Western philosophy has had two schools opposing each other, empirism and rationalism, which wasn't really attempted unified until Kant. So there's two modes of thought and most of the big ones are in either schools. EDIT OK not most, but many.