The first thing to do is work out what shape each diagram represents. Across each row, these are in turn:
EQUILATERAL TRIANGLE, UNIT SQUARE, BLACK CIRCLE,
RED SPHERE, YELLOW HEXAGON, GREEN TETROMINO.
Highlight the cells in each grid which contain letters that do not appear in the name of the corresponding shape:
What do we now have? The highlighted cells on these 8x8 grids of squares:
Are the squares on a chessboard that represent the furthest a chess piece can (theoretically) move from its starting position! We can see this more clearly by highlighting the start positions for the pieces in question (thereby fulfilling the enigmatic Step 1 of the puzzle instructions):
Now, we have identified 16 letters of interest - the same number as the number of "+/-" commands in Step 2 of the puzzle instructions. What we must do next, therefore, is:
Augment the letters in our 16 yellow squares by the number of alphabet positions indicated in the command list, like so:
U-18, T-18, Q-12, C+0, A+10, R-5, D-3, R+2, S-14, R+1, E+4, H+10, R-9, E+18, U-12, U-7
...which then spells out the message we seek (punctuation added)...
CHECKMATE, SIR - I WIN! - a remark fit for a gloating 'champion, with a smirk', as per the title!