According to your note, wouldn't that mean black moves first?
Starting position - mate using one piece

I'm not really understanding the instructions. Still, is this the right interpretation?
White seriesmates black moving only 1 unit: d2-d4-d5-d6xc7xd8=N-c6xb8xd7-c5-a6-c7#.
Check mate black by moving one piece(of white)
Note: black will only make a turn(move) when checked.
so in conclusion, this is not a legal chess game, the piece you can move can only be a knight or a pawn