Given int index;, an index into your 64-pin array:
The column digit is: (char) ((index % 8) + '1')
The row letter is: (char) ((index / 8) + 'A')
so:
Serial.print((char) ((index / 8) + 'A'));
Serial.print((char) ((index % 8) + '1'));
Is there a button to tell you the move is over, like on a chess clock? Or do you intend to watch all changes and infer the end of a move from the sequence of changes?
You may need to keep track of where each piece is. You may need to keep track of whose turn it is. You will certainly need to keep track of the previous state of the 64 sensors. That can be done in a single 64-bit integer or 8 bytes. You may need to keep track of the order of individual changes.