Pythagoras: Thank you ! Ambiguous Chess was born in January 2005, published on my web site, on chessvariants.com and some months later in the Variant Chess magazine.
Although it is a very simple idea, it came to my mind in a very roundabout way. By telling it I am a bit afraid to bore everyone with a long post, feel free to stop reading right here !

I read in the Encyclopedia of Chess Variants about a strange variant called "Unambiguous Three-symbol Chess", where the only moves allowed were those who could be written in three symbols in the English game notation. It gave me the idea of "Unambiguous Chess" where the only moves allowed are those who are determined by the arrival square alone (all ambiguous moves simply forbidden). This was probably a good idea for a problem stipulation (problem composers like strong constraints, which make it easier to avoid dual solutions), but not a good one for a playing variant (actually Unambiguous Chess is a forced win for White under the no-check rule).
Moving from Unambiguous Chess to Ambiguous Chess is not a very big step, still it took me something like five years and happened only when for some reason both Unambiguous Chess and the game of Quarto came to my mind in the same time - Quarto is an alignment game where you choose the piece which the opponent has to place on the board.
There were only two rules which were not obvious to settle, the castling one (argh!) and the promotion one. At first I had the "normal" promotion by the pawn's owner, but then a friend of mine rightly pointed out that it was more logical that the piece was chosen by the opponent, as the different promotions were different moves to the same square. I hope you will agree with this one :-)