so I don't think it's proper to speak of every high-level businessman or professional poker player, say, as a master rationalist.

I agree completely. I do not think of them as my pair, they were just a tool to help understand your pair.

People around here frequently use the word "rationalist" to refer to the people involved in creating or popularizing the theory of rationality, but it often happens that those people failed to fully internalize their theory

I now think I understand the pair you were trying to communicate. When I read great rationalist I think of someone who has successfully applied rationality over a great breadth of their life. So "one who practices rationality" but are not "one who produces results useful to rational decision-making" and those that "one who produces results useful to rational decision-making" but are not "one who practices rationality" have both only implement rationality in a limited breadth of their life and I would not have described either as great rationalists, at least when keeping all other variables equal.