The site is full of 'spoilers' for the book

Living Labyrinth

by Ian Stewart and Tim Poston

If you can't read St Matthew's Gospel because St Mark gave away the resurrection, don't explore further.

I like background on books:
let me in, and do not warn me again

or Go to where I can get the book.

The game of Shinsa

In the Old Tongue 新士 or 신사, this two-person game is popular in all regions and subcultures of Qish. It is played on a board divided into six-sided hexes, initially with the pieces (sa) laid out thus:

Board and pieces for Shinsa

They are shown here with their Shaaluy names: elsewhere in Qish, the names are less ecclesiastical, but the allowed moves are identical. Board sizes vary, and some variants include wyzands at fixed board locations, but the most popular form is that described here. Capture is similar to chess and checkers: land on a hex occupied by an enemy sa, which is then removed from the board. Landing on a hex occupied by one's own side is forbidden. As with the king in chess, victory ('doom') requires trapping the enemy Archflamen. At most one sa can occupy a hex. Unlike chess and checkers, most sa face in a particular direction, and a sa can turn six ways in its hex. A player can rotate it, but this counts as a separate move: it cannot revolve during transfer to a new hex. Players take turns to make one move at a time, with no extra-turn rules as in some checkers variants. The allowed moves of the sa are as shown below.

Moves for Shinsa

An archflamen can move to any neighbouring hex.
A high preceptor can move any distance in the directions of the neighbouring hexes, but cannot jump over an occupied hex.
A flamen can move forward or back any distance in the direction it faces, but cannot jump over an occupied hex.
A preceptor can move forward or back any distance to any hex of the colour it now occupies, but cannot jump over an occupied hex. Passing between occupied hexes is allowed.
A minorite can move to any closest hex of the colour it now occupies. Passing between occupied hexes is allowed.
A throng sa can move to the neighbouring hex in the direction it faces, unless that hex is occupied. It can move to an enemy-occupied neighbour it shares with that hex, capturing the occupant.
The specifically Qishi feature of shinsa is that the paired sa — all but the Archflamens and the throng — carry syntei. (Even on Qish, these are not physical syntei. Similarly, pieces move by finger power, not by their own legs.) Thus, if a black sa's move takes it to the hexagon occupied by (for example) a black flamen, the sa can continue through the flamen's synte, emerging in the hexagon occupied by the other black flamen: but only if it can continue its move and reach an empty or enemy-occupied hexagon, by moving in its allowed style; and only if the other black flamen is still on the board. (A throng sa continues with one after-kantasynte step, after the one step that takes it to the kasynte, if the forward hex is empty or an off-forward capture is possible.) Its direction, emerging from the kantasynte, is the direction of the flamen that carries it.
Similar moves can pass through via the black flamen-flamen or precentor-precentor syntei. Only a throng piece is small enough to pass through the synte carried by a pair of minorites.
If a black sa's move arrives at the hexagon occupied by a blue paired sa, it can either capture it as in chess (remove it from the board, and remain in that spot), or go through that sa's synte, removing both of the enemy pair from the board. In this case it remains at the arrival hexagon.
Vice versa for the moves of a blue sa.
If anybody feels inspired to implement Shinsa in JavaScript, Ruby, etc., with provision either for friendly one-on-one games or for elimination championships, we would be happy to host it on this site, with full credit to the creator(s): academically certified, or nice to link to on LinkedIn or a CV. Open source, please, so that people who want to develop (for instance) the form played on Samdal can build on what you do. If a community develops, Shinsa will need its own tutorials, example games, discussion forum section, etc.
If you make physical shinsa sets to sell, we will add a market place to this site to help you.

'Where do you get your ideas?' department
This was not revealed by thinking "What exactly are the Deacon and his Chaplain playing?".
Tim was reading a wonderful book on Indian history, and thinking about the original 'four players and dice' form of the game of chess. With syntei in mind, the syntelic game sprang into a first view: the names of pieces, and the hexagons, then came from the novel text that Ian had written much earlier.