story - What do chess and wordoku have to do with each other? - Clue Thirty-One

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"Aha! That's it," you exclaim, still holding the papers. "The answer is obviously [redacted]."
Having figured out the answer, you start looking over the rather bare-looking desk, still swiveling in the chair. Then, behind you, you hear a click. You stiffen. Slowly, you turn around, thinking uh-oh. Before you get all the way around, though, there's a loud SNAP and the legs on your chair snap.

You tumble on the floor, dropping the papers, covering your head with your hands. When nothing happens, you slowly stand up, looking all over the room. You don't see what may have made that click, but you do see that there is something on the ceiling.

You stand up and crane your neck. Squinting, you struggle to make it out. It appears to be a Sudoku board, along with four chess board. An odd combination, you think. Scanning the ceiling, you see a line of what appears to be instructions on the right:

What does chess have to do with sudoku? You'll see. Solve the sudoku, and then figure out what makes each chess board so... unique, let's say. I daresay that'll be impossibly, essentially. Can you figure out what you have to do after that? Good luck, Clue hunter.
-P. Oh

Here are the chess boards and sudoku board:

_{Boards generated with lichess. Sudoku puzzle originally generated by http://www.sudokuweb.org.}

Answer

The answer is:

LILY

This is obtained from:

Taking the most obvious* error on each chess board and using the letter at that position in the solved wordoku.

*Ordered by:
 • A piece in an impossible location (without considering other pieces);
 • Duplicate pieces;
 • A piece in an impossible location (taking other pieces into consideration).
Tie-breaking is done by using the one with more errors.

For the first board:

The pawn at G8 is in a position that is impossible for a Pawn. This corresponds to the letter L on the wordoku board, as solved by Beastly Gerbil. No other piece is in an impossible position when considered by itself.

For the second board:

There are two white Kings and two black Bishops on black. Also, several Pawns are misplaced without an amount of pieces missing to make it possible. The Kings and Bishops are the only ones that are duplicates.

The King at D7 is the only one of these that is also in an impossible position (double check). It corresponds to the letter I on the wordoku board.

For the third board:

The Pawn at F1 is the only piece in an impossible position without considering other pieces. That location is the letter L on the wordoku board. (This letter was given in the original board)

For the fourth board:

The white Bishop at F3 is the only piece out of place. The white King and Rook can reach those positions by castling. F3 is the letter Y on the wordoku board. (This letter was also given in the original board)

Putting these letters together, we get the solution:

LILY