Comments/Ratings for a Single Item

As I understand it, Pawns on any halfboard but the one they started on
move
away from the join. This after all is a continuation of the direction in
which  they joined that halfboard.
A small point of correction: 'any two-player game' should be qualified
by 'with an even number of ranks', ruling out Shogi. This is a pity
given the advantages for one-Bishop games generally through the use of
three-point turns. Shogi would need a neutral one-rank strip, with two
4-rank part-boards added in each move.

Rules can not be substituted for ALL games: it can be subsituated to any
game in wich pieces starts on different halfs of board (for example, i
can't imagine, how to play Chaturanga for 4 players and Tafl, using such
rules), also there are probably many things, wich don't allow to play some
games, using such rules. But, i think, most of games CAN be played in this
way, and it's a very good idea. Also i can suggest game for any EVEN
number of players: half of players starts on halfs of boards, wich have
ranks 1-4, another half starts on halfs of boards, wich have ranks 5-8, and
all boards of 1-4 are coupled with boards of 5-8, when moving piece to
another half, player may choose either.
Also i have one small question about original game: i suppose, it's not
important, who have left king and right queen, and who have right king and
left queen :) ?

Joining by reflecting is not so contrived. Imagine constructing the half-boards out of stiff cardstock or plastic, checkered on both sides so that the bottom-right square from each perspective is light. Use magnetic chess pieces in pairs so that they attract each other through the material. Bind several of these half-boards together with loops of string along the joining edge in an arrangement just like the illustration that opens the article. Now you join half-boards by flipping to two pages and ignoring whatever happens to lie in between.

But I said I was 'about to suggest'. That's because this arrangement causes the act of moving a bishop from the Green half-board to Orange, and then later to Blue, and then back to Green, to have the consequence of changing the Bishop's colorbinding because it has effectively been reflected an odd number of times. I still like the idea somewhat, but I think it is more important to have colorbound bishops than a symmetrical royalty-seating arrangement.

Your (Robert Price) idea is same as mine, however I think you need to either do it like Queens Left chess, or else allow bishops to not be colorbound.

I was wondering about pawns movement too like Bastien, but Gilman answered in a good way.

Using rules for shogi, since is 9x9 board (odd number of ranks), you need some way to know how to figure out the middle rank! One way could be, the middle rank is fixed and is always considered a part of the board. Using such a game with shogi also has a lot of other consequences: Rule of pawns movement mentioned in the paragraph above would also apply to nearly all pieces of a shogi game (王將 are the only exception). If you already have your own 歩兵 in one file, maybe you put together the boards that hide it so that you can drop another one anyways, and with boards rotated into place it can be caused even without dropping pieces into the board. Making a checkmate by placing 歩兵 into the board also is affected by which board is placed together.

With xiangqi, you can easily split the board according to the river, but then there is the condition of 將/帥 not being allowed to look at each other. Rules are required to consider this. For example, you can mean, you are not allowed to join together the boards which would cause such a condition, or you can use a 飛將 ("flying generals") rule, meaning you will take over the opponent's palace. The other thing is many name of pieces are different for each side, in xiangqi, such as 象 and 相. You can resolve this easily, by just picking one set of names, or just mixing them up whichever way you want.

It would be even more strange with Go. Again you need a fixed middle row. You could have multiple board pieces that can be joined together, although nobody owns one of them as opposed to another one. You can capture groups by picking which parts of boards to join, too. Rules about how you are allowed to lose your own pieces becomes more significant in this case. You could even play with three half boards but with only two players, even.