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I used the term "parallel universes" deliberately, and using the correct meaning for the implicit use of "dimension"; I was suggesting that the third dimension in this case isn't a vertical one through space, but a fifth dimension that runs through the four universes and ties them together.

That said, the change in name would probably be a good idea (even though any suggestion would require resubmitting under the new name and deleting this one). Personally I'd go with something like "Tetra Parallel Chess."