Yeah, The Duke is pretty interesting. Along the same lines, look at Onitama.
Setting aside my intrinsic love for board games, the aspect of this discussion which fascinates me the most from a Less Wrong perspective is the use of words and categories. How do we arrive at a distinction between whether games are "variants" or "in the same family"?
Each category has strongly-bound traits and weakly-bound traits, such as "a matrix of regularly-spaced locations where game materials can be positioned". Even the category of abstract games has traits bound to it, like deterministic non-randomness.
Almost twenty years ago, I made several custom Shogi sets. The kanji characters meant nothing to me, and I had to look them up on a chart each time I took a turn. This was poor cognitive ergonomics, and imposed an unacceptable cognitive load, distracting from play. So I replaced them on my custom sets, with a pie-chart-like diagram on each tile, which showed where the tile can move. I omitted the kanji completely. This was the only way I could convince beginners to play it with me.
When I finally went to a Shogi event and showed the set to Shogi players, they felt almost actively-opposed to its existence. The reason they gave, was that they played Shogi to take part in a long tradition, and they wanted new players to learn the traditional kanji characters before they have an opportunity to even begin to learn how to play a strong game.
Keep in mind, in the two-thousand-aughts, I was a being of pure authenticity-- "authenticity" as defined as opposition to tradition, or ritual, or doing things because others are doing them. I was a full-on Microsoft-hating partisan of Linux. I called myself "transhumanist". I was president of the Logical Language Group, a standards body for a utilitarian constructed language designed around predicate logic systems. I kept talking about alternative calendar systems, and abolishing the penny and normalizing dollar coins. And more than anything else, I talked about atheism. A lot. A traditional approach to Shogi frustrated me because it was un-optimized.
So I hope you will understand if, since then, I've preferred the phrase "chesslike games", because "chess variants" treats FIDE chess as if it were a Platonic ideal. It's selected as the prototype of the category because it's familiar. Its mind-share makes it the equivalent to what Facebook is to social media platforms. Are chess variants "variants of chess" instead of "the chesslike family" because we have a traditionalist's loyalty to FIDE rules? It's not like a platonic solid. It's not.
And honestly, why should it be? Is Go a "Tic-tac-toe variant"? Tic-tac-toe is closer to a Platonic solid, from the criteria of simplicity. So are Symple, Hex, and the rest of the family. But we don't use minimalistic simplicity as the criteria. I think I see mind-share as the most common criteria. And this is why you get into pathologies like "true" 3D chess, which takes several days to play, it's impossible to catch the King, and it scales outside of the human mind. All in order to keep "true" to familiar FIDE orthodoxy, detached from the quality of the gameplay experience. A 3D chesslike game is a lot of fun, if you completely discard whatever you have to discard to make it playable and fun. "True" this, and "true" that, is a mental pathology.
I'm a published board game designer, and my design criteria only have to do with factors that make a game easy to teach, easy to set up, not take too long, and provide a depth that emerges from a rich set of simple interactions.
I'm interested in your concept of Chess feeling like it's complete, as if it has completed a platonic solid. You remedied its incompletions with the Cardinal and Marshal, but Omega Chess attempts to fill in the lack of leapers by introducing the Champion and Wizard. The design of Omega Chess was similarly motivated by this sense of completion, but it seems its design locates the gaps in different places from where the design of Grand Chess locates the gaps. Did you consider this? And how did you come to this conclusion?