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I had the same question of whose king goes on the left or right, and I was about to suggest an alternative: The author calls for you to push two half-boards together by rotating one into place above the other. I was about to suggest reflecting it into place (and inverting the checkered coloring) instead; now you can let everyone's king start on the e-file but the two-player case is still just like FIDE chess.

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.