Drop everything--CRAZY new offers are in the HOUSE!
Answer: MATCH OF THE CENTURY
Kevin Zhou (Kaz)

First, we solve the 8x8 dropquote. Solving the dropquote is easier upon realizing that the grid is full of chess-related words.

The title of the puzzle clues crazyhouse chess, a variant of chess where a player can drop pieces on the board. The only caveat important for this puzzle is that pawns may not be dropped on the 1st or 8th ranks.

For each chess position, the color of the "Mate in __" text corresponds to a color in the dropquote. The solved dropquote tells us what pieces we may drop:

BISHOP
KNIGHT AND PAWN
ROOK AND PAWN
KNIGHT AND QUEEN

Using these pieces, we find checkmate for each position. Finally, the squares that the pieces are dropped on correspond to squares on the solved dropquote, which allow us to extract letters. Notably, a normal piece move is not extracted.

Position Solution Extracted letters
B@b7# M
B@a1# A
B@h5+ Ke4 B5xg6+ (Kf3 Bh5#) Kd5 Bf7# T
N@e8+ Kh6 @g5# C, H
@a3+ Kb5 dxc4+ Kb6 N@a8# O, F
@d7+ Kf7 @Nh6# T, H
@e7+ (Kf7 e8=Q#) Kg8 e8=Q+ Kh7 R@h8# E, C
@e7+ (any) R@g4# E, N
@Nd7+ Ke4 Q@h7# T, U
N@h4+ Kg7 Nf5+ (any) Q@g7# R, Y

Finally, reading the extracted letters in order gives the answer.


Author's Notes

I was thinking of having an extra step of dropping all pieces using gravity. However, it was way too difficult to construct.