Atrio

Atrio is a 2000 game from Christian Gibon, published at LM Créations and Murmel Spielwerkstatt und Verlag AG.

The game is played on the following board (I was unable to find the initial setup),

Each player starts with three marbles, two regular and one special.

• The regular marbles can move one space in each direction (orthogonal or diagonal)
• The special marbles can move one or two spaces in the same directions

The goal is to place your marbles inside the center 9x9 area (inside the interior circle), or else to push out one enemy marble out of the board (outside the exterior circle).

If the moving marble is adjacent, in the moving direction, to an enemy marble, it will push the enemy marble. This is valid only if all spaces where the pieces move thru are previously unoccupied. The Ko rule applies, the next player cannot use the same pushed marble on the opposite direction of the previous move.

Domain

Domain, aka Boomerang and Chameleon, is a 1982 game by Claude Duvernay, and published in several companies.

There are two sets of Tetris pieces. Here is the blue set:

And these are the rules:

Domain was reviewed by Sid Sackson at GAMES #37: 

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Poliminoes are a much-explored subject in Recreational Mathematics. A good book about the subject is 1965's Polyominoes: Puzzles, Patterns, Problems, and Packings by Solomon Golomb.

 

 

Poliminoes (especially trominoes, tetrominoes and pentominoes) appear in many abstract games. BGG lists more than 100 abstract games using poliminoes.

 

Probably the most successful one is Blokus,

 

which also provides a very nice material set to design and experiment with new tiling games.

Canyon

Canyon is a 1972 game by Frank Ullmann and Tom Werneck, published at Heyne.

Each player has 15 pieces that must be placed on the spaces inside the triangles marked by cells 1, 5 and 11.

Rules:

A piece can move to an adjacent space in any direction: forward, backward, diagonally, or sideways.

It is also possible to jump over one or more friendly or opponent pieces in any direction, provided the next space is free. You can jump as many pieces as desired.

Each opposing piece that is jumped is captured.

The central zone, the canyon, is impassable. Players must go around it to the left or right. Numbers on the edges of the board indicate the value of each row based on each player's perspective.

The players’ goal is to move as many pieces as possible to spaces with high values. 

The game ends when one player has moved all their remaining pieces to the rows with the highest values. Both players add up the scores of the spaces occupied by their pieces. Each piece scores the value of its row. The player with the highest score wins the game.

Brainline

Brainline is an uncredited 1970s game published by Berliner Spielkarten and Palitoy.

 BGG has this description of the rules:

A two player abstract game played on a 7 by 9 array of hexes. Each player has four pegs of his colour on the specified starting hexes. On his turn a player may move any one of his pegs any distance in a straight line but may not jump any other peg. The object of the game is to be the first to get all four pegs of your colour in a straight line. They do not have to be adjacent but there must be no opponent pegs between them.

I've also found this review in Games & Puzzles,

Babylon

Babylon is a 2003 game by Bruno Faidutti, published at Interlude (among others).

The game does not have a board, only twelve stackable tiles (three tiles for each one of four colors).

Initially, all tiles are placed in the gaming area. Let's denote a single tile as a stack of size one.

Rules:

• On her turn, the player must place an entire stack on top of another.
• A move is valid if either:
• both stacks are of the same height
• both stacks have the top-most piece with the same color 
• Wins the player making the last move

This is a game that seems very amenable for analysis using Combinatorial Game Theory. But I'm not aware of any article studying it.

Peace

DIY Draughts

Do-it-yourself draughts, or Dames en Kit, is a c.1890 game by Walter Sanders,

diagrams from Jeux Stratègie's page

Rules. Each player has two pieces and 20 tiles (one light and one dark set).

First phase: On each turn, each player places (a) a friendly piece on an empty same-color tile, (b) a friendly tile at the side of another already placed tile, (c) or both.

Second phase: When all pieces and tiles are placed, pieces are allowed to move to any adjacent empty tile of its color (including diagonals). 

However, in both phases pieces also have the option to capture. Pieces capture by jumping one or more consecutive enemy pieces, assuming there is an immediate empty tile of its color to end its move.

Captures are multiple, i.e., after a capture, the player may continue capturing with the same piece. And, like Checkers, captures are mandatory (if there are several options, the player can choose which). Captures are mandatory in both phases.

• Notice that it is possible to place a tile, opening a capture option, that must be executed in that same turn. However, even if it is possible to place a tile in these conditions, players might choose not to.
  

Wins the player that captures or blocks all enemy pieces. If the interactions between pieces are no longer possible, wins the player with more moving pieces (blocked pieces do not count). Otherwise, the game is a draw.

Example: in this diagram, players cannot interact with each other. So, Black wins since he has two moving pieces against just one moving white piece.

The game appeared at Roger Millington's Games and Puzzles for Addicts (1979),

The game also appeared in Jeux et Stratègie #42 in 1986: