They're reasonably evocative (both of the pieces' actual nature and of the traditional shapes used for them), I think.

The rook/castle, which moves orthogonally, is represented by a square made out of orthogonal lines.

The bishop, which moves diagonally and traditionally has a kinda-triangular mitre on its head, is represented by a triangle with diagonal lines for sides.

The knight, which moves in a funny way and is traditionally shown as a sort of horse's head, is represented by a quarter-circle which is unlike all the other shapes (less symmetrical, mix of straight and curved lines) and actually quite similar in outline to the traditional horse's head.

The king, which is usually shown with a cross on its head, is represented by a cross.

The queen, which moves like a king but more so and which is usually shown with a many-pointed crown on its head, is represented by a many-pointed star (a bit like that crown, and also a bit like the king only more so).

And the pawns, which are weaker than all the other pieces and traditionally smaller than the others, are represented by little circles, smaller than the other pieces.

I just hung a piece to the opponent's knight because I didn't realize it was a knight.

Its completely unplayable for me.

it's like you are explaining how somebody can invent a new alphabet that is "evocative" so we should accept using it instead of the alphabet we already know.

or to put it another way, Staunton.