Anime

Let's look at the chess board where bastard principal interferes with Ayanakoji's move:

The situation is Sakayanagi's Black is "threatening" 1. ... Qxg2 check "Threatening" in quotes because as we see in the story, the obvious defensive White is move 1. gxf3 ?

The question mark because it's a poor move because moving the Pawn out of the way allows:

2. ... R-g6 ch

and maybe

2a. Q-g5 Rxg5 ch But this extra move just delays the inevitable

3. K-h1 Bxf3 mate

Let's talk about Ayanakoji's intended move after the original setup:

1. Q-g5 by threatening checkmate 2. Qxg7, Ayanakoji sets up an exchange of Queens, and maybe other pieces.

Any reasonable scenario after that results with his White having a significant material advantage.

If Black responds with

1. ... Qxg2 ch then

2. QxQ BxQ

3. KxB ...

And the end game starts with White having 2 Rooks and a Bishop, which should easily overwhelm Black's one Rook for a White victory.

If Black takes White's Queen with the pawn

1. ... Pxg5 then Black's Queen is also lost

2. Pxf3

and we're left with...

The doubled black Pawn on the g column blocks Black's Rook from moving to g6 check, and also therefore prevents starting the checkmate process in the first scenario.

White has a significant material advantage with 2 Rooks, and a Bishop against Blacks 1 Rook and 1 Bishop.

Basically, even at the beginning of this scene Sakayanagi's Black was already in a losing state being down 1 Rook, so any scenario with an even trade of pieces was to Ayanakoji's advantage.

The only way for Black to win was for White to make a huge mistake which bastard principal provided for her.

p.s. Thanks to chess.com for providing a web-editable chess board.