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Note that these are just necessary conditions. Not satisfying any of those will be a deal breaker, but satisfying all of those will not necessarily mean the article is ready for publication.

I don't think that the rules are already clear and easy-to-understand.

First of all, it should state the initial array and the pieces of the game (I somehow infer it is the standard chess pieces in the standard initial area).

With all kind of swaps: What are the moves of a pawn being swapped to the first rank? Has it double or even triple moves available, or does it just a single step to the second rank? When it has stepped to the second rank, has it
a double move or not (a strict reading of the FIDE rules having "original square" in their wording would allow only a single step, since it is subsequent. Quite hard to track by looking only on the board)?

With inner swaps, it should state if a swap between two identical pieces (e.g. two knights) is allowed, creating the possibility to voluntary cede a tempo. This option would change some endgames (e.g., making two knights and king against king a win instead of a draw).

I think the bishops rule is theoretically flawed, since it is possible to have two bishops of the same field colour by pawn promotion (it is just really unusual to promote to a bishop because promotion to some stronger piece is almost always preferable).

In the FIDE laws of Chess it says:

3.7 a. The pawn may move forward to the unoccupied square immediately in front of it on
the same file, or
b. on its first move the pawn may move as in 3.7.a or alternatively it may advance two
squares along the same file provided both squares are unoccupied, or
c. the pawn may move to a square occupied by an opponent’s piece, which is
diagonally in front of it on an adjacent file, capturing that piece.

(emphasis mine). But this is just one possible formulation out of many equivalent ones, and one cannot be sure that in the future or elsewhere (e.g. in other languages) the formulation would not be different. (This is not without precedent; in recent time the wording of the rules for castling was changed, to make it more explicit that 'vertical castling' with a Rook obtained from promotion is not allowed.) I would interpret "on its original square" as an absolute statement about location irrespective of prior history. (But then also meaning not just on 2nd rank, but also in the same file.) That would be another matter if it said "still on its original square", which would imply it must have been on that square all the time.

Are you sure about the two Knights? I think the problem there is not so much shedding a tempo as that you are a tempo short to beat the stalemate.

There is already another variant called Swap Chess.

The author, Guillermo Garcia, has updated this page.