'The shortest game ending in mate must be 2. Bd3-g6, and except for move order, the rest of the moves are forced.'
I do not understand this assertion. How can Bd3-g6 be move 2? The g2 Pawn has to be moved (move 1) before the Bishop can even reach d3 (move 2), so move 3 is the earliest that the Bishop can actually leave that square. I am also intrigued to know how putting it on g6, where it is still under double threat, helps. If the Pawn row were YPPYYPPY rather than YYPPPPYY, giving only a single threat to g6, it would be more understandable but even then Black might be able to do something before White gets their Queen in place.