That makes good sense. If you know the original location of the pieces and they only move one-at-a-time, then it's easy for the computer to keep track of the moves.
But, as you state, this requirement is much more difficult since you have to detect seven difference piece values as well as random location. Don't know what the best solution for that is. Perhaps some type of optical approach?
For example, you might have one of seven simple bar-codes on each piece (since you only need to detect seven different types of pieces) that could be detected by a simple optical scanner under each piece location. But that still could get expensive for a 15 x 15 location Scrabble board.