Although Doublestep Chess changes just one rule, there are several paragraphs discussing the rules because of the surprising implications of this single change.
Doubletime Chess intereprets the rule of doublemoves differently, with more surprising implications.
In Doublestep Chess, everybody can make a doublemove, not just unmoved Pawns.
To make a doublemove, a piece makes a non-capturing move, and then it makes another. For example, 1. Nb1-c3-e4 is a legal doublemove.
You'll notice that when a Pawn makes a doublemove, both the moves must be in the same direction, because in fact a Pawn can only move in one direction without capturing; but the FIDE rules do not prohibit other types of pieces from changing direction when they take their doublemoves.
Doublestep Chess may sound like a game that belongs in Limited Doublemove Chess, but in fact Doublestep is a single-move game in which the pieces make doublemoves, not a doublemove game in which both moves must be made by the same piece. There is a big difference, as the next section shows.
According to the rules of Fide Chess, when the first move of a doublestepping piece lands on a square attacked by the foe, the doublestepper can be captured en passant: the capture is performed by as though the second step had not been taken.
Doublestep Chess follows the rules of FIDE Chess, and allows all pieces to be taken en passant if they make doublemoves; but please notice that only a singlestep move may be used to perform an en passant capture.
In FIDE Chess, only Pawns and Kings can be taken en passant, but that is because only Pawns and Kings have any sort of doublemove.
(Notice that Castling is already a special doublemove, and so in Doublestep Chess you may not play O-O-O and Kc1-b1 all in the same move; since Castling is a doublemove of sorts, in FIDE Chess you may not play O-O-O with d1 attacked lest your King be taken en passant.)
You should be aware that the move e3-e4-e5 is a legal doublemove.
The first part of a doublemove must, as always, be a non-capturing move.
Clearly, the rules of FIDE Chess require that if the second part of a doublemove was a capture, then making an en passant capture in response uncaptures the originally captured piece and makes the wronged party whole. (The piece that appeared to have been captured was in fact just held hostage.)
For example, after 1. Nb1-c3-e4? a7-a6? 2. Ne4-f6xe8 Ng8xf6 en passant, the Black King reappears on e8, safe and sound. Although this result may seem a bit odd at first glance, careful calm consideration will convince you that no other result is possible under the standard laws of Chess.
1. Ke1-d2-d3, Ke8-d7-d6 2. e2-e3-e4+, Kd6-e6 3. Kd3-c4+!
Now Ke6-d5xc4 is not legal because of e4xd5 en passant.
3. ... Ke6-d7 4. e4-e5-e6+ (e4-e5+ is simpler) Kd7-e7 5. Kc4-d4 Ke7-e8 6. Kd4-d5-c6+! (Kd4-e5 would be stalemate).
This simple endgame demonstrates how the doublemoves and en passant work together.
This simple endgame illustrates a major characteristic of Doubletime Chess: as soon as the position opens up, Rooks become incredibly powerful. En Passant works only when the first step of the doublemove lands on a square you attack; against Rh1-e1xe8, control of e7 is no help at all.
Games of Doubletime Chess will often be short, and the computational burden will be great: you must think hard before opening the position or allowing it to be opened. I used to like this sort of game when I was younger, but now I prefer a simpler game -- the tactics of FIDE Chess are as complex as I like, and I feel that more complex tactics take something away from the strategy of the game.
However, I used to like this sort of thing, and you might like it now.
Doubletime changes two rules, but always in the direction of greater freedom of choice. We all love freedom; I think everybody in the world should be free to agree with me.
How can one not like a game in which pieces that have apparently been captured may in fact have not been captured at all? And the balance between offense and defense, is it not wonderful how it is maintained by the possibility of en passant captures freeing the hostages?
I cast my vote for Doubletime Chess, but I'd rather play Doublestep Chess because I feel the tactics in Doubletime are too intense for me.