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Darmani comments on How to always have interesting conversations - Less Wrong
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Ok, then. Here's my attempt.
Intrinsically interesting topics are topics which satisfy the following criteria:
1) The topic cannot be discussed by an adult human of average intelligence without putting in some cognitive effort and attention. (If you can be busy thinking about another topic while discussing it, then it probably isn't intrinsically interesting). If the topic cannot be discussed by a human of average intelligence then this condition is considered to be met.
2) The topic must have objective aspects which are a primary aspect of the topic.
3) The topic must have some overarching theories to connect the topic or have the possibility of overarching theories explain the topic. Thus for example, celebrity divorces would not fall into this category because they are separate unconnected data points. But differing divorces rates in different income brackets would be ok because one could potentially have interesting sociological explanations for the data.
4) The topic must have bridges to many other topics that aren't simply a variation of the topic itself. For example, AI bridges to programming, psychology, nature of human morality, evolution, neurobiology, and epistemology. In contrast, D&D rules don't connect to other topics in any strong way. There are some minimally interesting probability questions that you can ask if you are writing a quiz for an undergraduate probability course but that's about it. Most of the other topics that it is connected to are still variations of the same topic such as say what a society would look like in a universe that functioned under standard 3.5 D&D rules.
I doubt that. Before I had finished the paragraph, things that came to mind included board games, what underlying skills transfer between different board games and RPGs (from empirical evidence, they exists and are large), what the appeal of roleplaying a fictional character it is, which different desires roleplaying versus powergaming satisfy, what makes a character attractive to roleplay, what makes a roleplay performance fun, what makes a D&D setting enticing, how to create an enticing D&D setting, whether the most fun is had when the DM does a good job of almost killing the characters (as someone told me), and more. These, of course, give hooks to combinatorial game theory, personality, improv acting, fiction writing, and fun theory. With the possible exception of personality (though it's a small leap to MUDs and the Bartle 4, so probably not an exception), all of these play quite important roles in D&D.
I suppose I'm muddying it a bit since some of those things are connected to D&D but not directly to D&D rules, though your original post simply mentioned D&D.
Knowledge is connected enough that I'd be quite impressed if anyone could find (or, heck, invent) a topic which fails criterion 4.
Even D&D rules connect to the general problem of creating games which are understandable and playable and the problem of creating reasonable facsimiles of reality - these contrast in an interesting way with the scientific problem of creating computationally-tractable models which predict reality, for example.