This is a really interesting puzzle and the first observation is that the message that can be seen is "your challenge is to figure out why this grid is eight by eight"
Now we consider only the different colours which are available - "yellow, green, blue, red, brown, white, purple" i.e., 7. Note if we don't consider white we have 6 colours.
Incidentally,
6 is the number of different types of pieces that a chess game has "King, Queen, Rook, Knight, Bishop and Pawn".
This gives us the possibility that each colour represents a difference chess piece.
Clearly knowing the movement of knight -- purple is knight [moves such as R--E, H--I, etc are all knight moves]
Similarly, brown is bishop h1, b7, a6, c4, d3, a7, b8 [standard chess coordinate lingo]
Green is a rook [a3 b3 b8 h8] all horizontal and vertical movements
Yellow has to be queen
This leaves us with pawn and king. Since, king moves only one square at a time we can quickly figure out blue is king (it began with castling!!!) and red is pawn (a4, a5, axb6, bxc7, c8=q promotion qc3, qg7, qg5)
So, we have found that each colour represents the movement of a chess piece due to which this is a chessboard in actuality.
Also, a chessboard is 8x8 which is why this board has to be an 8x8
The tag left out was probably chess