Calvinball: An awful lot of games played in the Empire are like this from our perspective, by virtue of having been designed to satisfy the game-playing urges of people with, well, transhuman intelligence. For example:
One of the simplest is the card game ómith. It’s like poker, except with six twelve-card suits on an elemental theme that the game itself shares (the suits are clouds, coins, droplets, flames, pillars, and staves) and a major arcana, plus a variety of metarules and dice-controlled variations, and a scoring system with an incredible number of special cases.
Larileth, or sigillary, which would most closely resemble mahjong, had mahjong been based on a set of combining rune-constructs devised to reflect the aspects of the universe as defined by (in Earthly analogy terms) a mash-up of Hermetic magic and qabala.
Ithréth, which is a sort of dynamic four-dimensional go, metaphorically speaking. (The lack of four-dimensional playing boards and four-dimensional spaces to keep them in adds an extra level of complexity once people start making moves ana and kata, which is where much of the true subtlety of the game lies. It’s much more pleasantly complicated than the “four-dimensional” games in which pieces just time-travel, for example.)
Iandaër, which is a battle simulation game that is on the one hand like chess, but on the other hand resembles taikyoku shogi rather more closely. It is thorough.
There’s also mírlathdaër, the favored game of AIs and other digital sapients. Which is essentially Nomic, only as played by entities which can successfully manipulate rule lists gigabytes or even terabytes in length in real-time. (For extra fun, there’s the simulation version where you do this with physical laws, and the point of the game is to create the most interesting simulated universe. The only acknowledged win condition for that one is to get intelligent life to evolve in the simulation without using any special cases; no-one’s actually won it yet.)
And then there’s kírasseth, the generally acknowledged monarch of eldraeic games; it requires several interrelated boards, sets of cards, dice, and some specially made mechanical computer-randomizers, it is self-referential inasmuch as the players, the rules, and the game itself are all also pieces within the game, to play with any degree of competence requires an astonishing mastery of everything from scientific principles to mythic symbology, and its most commonly used set of victory conditions include that any win which is insufficiently elegant and aesthetically pleasing is actually a loss. It is, of course, incredibly popular – at least to watch.