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A game rule is not a collection of words, it's an abstract specification of how the game transitions between different states. People who are playing Chess according to rules written in English and people who are playing Chess according to equivalent rules written in another language are playing "the same game", regardless of the fact that different words are used to describe it.

By the same token, "pawns may move 2 spaces forward on their initial move" and "pawns may move 2 spaces forward when beginning a move from their second rank" are the exact same rule in the context of FIDE Chess, because "the rule" is actually just a specification of which game states can transition to which other game states, and the set of possible transitions is the same in both cases.

They are different rules in the context of some Chess variants because they no longer describe the same set of state transitions. When someone is inventing such a variant, it is reasonable and appropriate for them to choose whichever generalization of the rule is best for their variant, regardless of which exact words someone somewhere decided to use to describe the original rule.

Though game designers who hope eventually to release expansions for their games should definitely think about how their rules will ultimately generalize in order to avoid headaches down the road...

If you change pawn rules to "pawns being able to move 2 steps while on second rank", this will ends with the same results because the pawns start on the second rank and will not be able to go to back to second rank later.
But this doenst means the rules are the same. As a example in chess with different starting setups, where some paws are not on second rank, this would change the things.

r..r..q.
........
.....n..
R.......
......k*
........
b..N...R
K...B...

Mr. Zanotelli raises an interesting point. His is indeed a possible way to apply the FIDE Pawn rules to the changed circumstances of this game. But Peter Aronson's way is equally valid. In the case of FIDE Chess, they are equivalent statements of the same rule, as a Pawn cannot make its first move from any place other than the second rank, and a Pawn on the second rank cannot have moved previously--neither of which conditions apply to the Pawn moves of other pieces in this game.

This variant assumes pawn can move 2 squares forward without capturing while he is on second rank.

But f.i.d.e chess rules 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"
http://www.fide.com/fide/handbook.html?id=124&view=article.

So this means the pieces would be able to move 2 squares foward on their first move, provided both squares are unoccupied.

Or, if you include the part "pawn may move as in 3.7.a or alternatively" on rule 3.7b, they would be able also to move one square foward in their first move if the square is unoccupied.

'Note that pieces that can move orthogonally forward more than one square
(the Rook and Queen) never use the Pawn's double-move ability, and so
can
never be captured en-passant, even when moving two squares forward from
the
2nd rank without a capture. '

An interesting further variant that would weaken rooks and queens could
ignore this.