This design doesn't account for many special qualities and behaviors pieces exhibit. It doesn't indicate that
* while pawns do capture diagonally (forward), they are pushed forward in straight line
* they can capture en passant
* they can move by 2 squares from their initial file, and only from the initial file
* they can be promoted to another piece
* Knight moves are not inhibited by the presence of other pieces (unlike any other piece, a Knight can "jump over" pieces)
* castling
* special status of the King (unless it's conveyed by that circle in the middle, but it's not nearly as readable a symbol as a crown)
So this design kind of works if you already have complete information from elsewhere, but isn't that great if it were your first source of info.
It also loses the poetic aesthetics of the traditional pieces, with queens and kings and bishops etc.