Duell

Duell, aka Conquest, is a 1975 game by Geoffrey Hayes, published by Alga (among others).

The game is played on an 8x9 board. It uses dice, not as random generators, but as pieces. Each army has eight regular dice, plus a 'key piece' with one dotted star on every side.

The setup is as follows (with all faces 4 facing inwards):

The rules:

• Regular dice move by 'tumbling' their faces over the next empty square (there's no diagonal moves; there's no jump over other pieces).
• The initial move must be forward or backward
• Pieces can also turn right or left during the move; this can be done just once during the move
  
• The number of moves is given by the die's top face; the piece cannot stop until the entire move sequence is done
• Key pieces can only move one square per turn (after all, all their faces have a one)
• Capture is by replacement and is only possible at the last square of the moving piece
  
• Wins the player that captures the enemy key piece; or moves his own key piece to the initial square of the enemy key piece (so White's moving from e1 to e8, or Black's from e8 to e1).
  

move examples from the rule book

Some hints given by the rule book:

• It is sometimes possible to approach one square from two different paths.
• Your choice of path will determine what number will be on the "top face" of your piece at the conclusion of the move.
• Your strategy can include planning for a subsequent move if you can control the top number and space location.

Here's a review from GAMES magazine #2: 

And from Games & Puzzles #48:

There are not that many abstract games using dice as pieces. We already mentioned Chase (1985) here in the blog. Other examples are Mojave (2004) and Cublino (2006).

Tris

Tris is a 2006 game by Daniel Solis.

The game is played on an 8x8 board, initially empty. Each player has enough pieces of one color (probably 40 is more than enough).

Rules:

• On his turn, the player either:
• drops a friendly piece, on an empty square, at the first/last row or vertically connected to another piece (or either color)

 all legal next drops shown

• moves a piece to a horizontally adjacent empty square
• then, the piece 'falls' until meeting another piece (falls in the direction of the edge supporting its column of vertically connected pieces)
• if there were pieces on top of the moving piece, those pieces also 'fall' 

all movements available

• If, after the drop/move, an orthogonal or diagonal 4 in-a-row of pieces of the same color is made, those pieces are removed from the board (cf. next rule for exceptions)
• the remaining pieces fall accordingly, which might produce more 4 in-a-rows, and so on...
• Fixed pieces: the pieces at the first/last row are fixed and cannot be removed
• when a row is full, those pieces also become fixed
• A player wins if either:
• his first four rows are full
• twelve of his pieces are removed
  

Comment from the author: Pretty simple game here, essentially taking elements of Tetris and Connect 4 and laying it flat on a board instead of vertically.

Hexagonia

Hexagonia is one of the first two hexagonal Chess in the literature^(*), c.1860. It was published by Jaques & Son, and its author is possibly J. W. Smith [1].

A new game for two players, played on a board divided into hexagons. Each player had fourteen pieces, representing infantry, cavalry, and artillery, and one principal piece, the King. The various pieces have certain moves on the board analogous to those of a real army, and the game is won by the player who first succeeds in placing his King (without liability to capture) on the central hexagon.

In Cazaux and Knowlton's A World of Chess, [2], the game is described. Each army is composed of one King, two Cannons, four Knights and eight Pawns. However, it is not known how the pieces moved. The book also refers that this game appears to have been invented, some years earlier, in New Zealand.

The book also includes the following quote about the game (page 377):

The last game which we have to notice is undoubtedly the most scientific of the lot, and somewhat resembles chess. It is called" Hexagonia," and is published by Mr. Jaques, of Hatton Garden. The board is in the shape of a hexagon, and contains hexagonal figures, painted red, blue, or white. Two play at this game. To each combatant is given a king, four knights, and two pieces in the shape of cannon, called artillery, and eight pawns, or pieces of infantry. Each piece has a different mode of moving, and can capture an enemy; and the object is to place the king on a gold square in the centre of the board. This sovereign can never be taken, but can be checked as in chess. The reader will gather fom this that much head-work and tact can be brought into play in this game, and that a knowledge of chess is often highly advantageous. We have endeavoured somewhat briefly to state the chief points of the new in-door games. We feel sure that they are varied enough to please the tastes of everybody, and we sincerely hope that our youngfiends may enjoy many a pleasant hour in the enjoyment of the intricate manoeuvres that these games involve" (Edmund Routledge, "The New Winter In-door Games," Routledge's Every Boy's Annual, an Entertaining Miscellany of Original Literature, George Routledge and Sons, 1866, New York, p. 35)

Pritchard's book, [3], also refers to the game: 

Hexagonia (Proprietary game, John Jaques and Son). Published in 1860 according to van der Linde, and allegedly awarded two prize medals in 1862, the game was in fact published on 23 September 1864 and registered at Stationers’ Hall the following January. 127-cell hexagonal board, central cell distinguished. Each player has 1 x King, 2 x Cannon (artillery), 4 x Knight (cavalry), 8 x Pawn (infantry). The moves of the pieces are not recorded. The object was to get one’s K safely to the central cell.

About the piece's moves. The King, Knight and Pawn moves are directly translated to hexagonal boards. The Cannon however could have been like a Rook, sliding rows of hexes, or like Bishops sliding thru diagonals, which might explain the use of three colors in the Hexagonia board (since it makes it easier to follow these diagonals). Both hypotheses for the Cannon would be stronger than the Knight's, which is compatible with their smaller number (two) compared to the Knights' (four). However, this is just speculation.

Since the game's goal is not to capture or stalemate the enemy King, it's arguably not a chess variant, but most of Chess themes are here, nonetheless. The first known hexagonal Chess with checkmate was 1910's Mars by M. van Leeuwen and published by F. H. Ayres.
______

(*) the other early Hexagonal Chess (also without checkmate) was designed by Thomas Hanmer Croughton, c.1853.

[1] Michael Thompson, Hexagonia, https://michaelthomson.org/game/hexagonia
[2] Jean-Louis Cazaux, Rick Knowlton - A World of Chess (2017)
[3] David Pritchard's The Classified Encyclopedia of Chess Variants (2007)

The commercial offsprings of Chess: Ploy

Ploy, aka Imperium, is a 1970 game by Frank Thibault, published by 3M among other companies. 

The initial setup:

The rules by Mats Winther from his Zillions implementation:

The goal is to capture the enemy Commander, or reduce the opponent army to a single Commander. Each piece has an indicator which determines at which directions the piece can move. This can be altered by rotating the piece 45 degrees, left or right (a direction move). Rotating the piece costs a move.

Each player has three Shields, five Probes, six Lances, and one Commander. The Shield moves one step and has only one movement freedom at any time. The Probe slides two steps and has two freedoms. The Lance slides three steps and has three freedoms. The Commander has four, but can only move one step.

A player must either make a direction move or a motion move. The three Shields are the only pieces that can perform a direction move immediately after a motion move. Capture occurs by displacement

Winther also includes some tactical advice:

This game seldom ends in a draw. It is sometimes worthwhile to sacrifice material if you can gain an attack on the Commander. When the pieces become scarce, the Commander is more vulnerable to attack. As it can only move four ways, it cannot easily escape. The Lance with the three forward directions is especially suited to attacking the Commander. Remember that you can also win by capturing all enemy pieces except the Commander.

The game can also be played with Ludii.

The official rules:

Here is a review of the game at Games & Puzzles #22:

The game was seriously promoted as shown by this full-page ad in The General magazine #13:

There is a similar game, but played on a hexagonal board, Michael Flynn's Omnigon (1998):

More information about this game at chessvariants.com.

The commercial offsprings of Chess: Smess

Smess, aka All The King's Men, is a 1970 game by Perry Grant and Reuben Klamer, published by Milton Bradley among others.

The game is played on this 7x8 board. Each army has twelve pieces: One King called Brain, four Numskulls, and seven Ninnys. Initially, the two Brains are placed at d1 and d8. Each Brain has two Numskulls at each side, and the seven Ninnys occupy the second row (just like Chess pawns).

The rules:

• On her turn, each player moves one friendly piece in a direction printed on its current standing square.
• Brains and Ninnys move only one square per turn,
• A Numskull can move in a straight line as many empty squares as possible
  
• Nb: only the initial standing square determines the possible moving directions
  
• Captures are by replacement (and not mandatory, just like in Chess).
• A Ninny that reaches an initial square of an enemy Numbskull is promoted to a previously captured Numbskull (if there's no Numbskull captured, the promotion does not happen).
  
• Wins the player that captures the enemy Brain. The game is a draw if only the two Brains remain on board.
  

The game was also known as Take the Brain. There's a review of it in Abstract Games Magazine #9.