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"All `double move' variants, I had known until then allowed the player to move different pieces."
I am almost sure there are 2 moves variants that only allow you to move the same piece.

But YES they aren't 100% like your variant.
If I remember one variant I saw allowed the player to make just one move (instead of the 2 ones) if he wanted.

What about the other rules of chess, including en-passent, three-fold repetition and the 50-move rule? Can you add that in?

Hi, Eric.  Thank you for pointing out this oversight and for calling my attention to this page.  I have updated it to address your questions, as well as how white's first move of the game should be handled, and made some additional revisions to improve it (such as adding the diagram.)

As I mentioned in my update, however, we do not know for certain how this game was played in 1996.  What is written is my best guess, along with justification.