This puzzle consists of five different games, where white can win with a single move, or they can provably lose with a different move. The flavor text indicates that the losing move is the one required for the puzzle, and in fact, solving for the winning move hints this again.
Connect 4 – If white drops into column W, they win; if they drop into column I, grey drops in the same column and wins. 
Eleven Men’s Morris – White slides their center piece along the O to make a mill and win. If they move their top piece along the N line, grey moves their piece diagonally along the V line and creates their own mill. 
Dots and Boxes – If white draws the line along the R, any move by grey gives up the remaining six boxes. If white takes either E, grey takes the other, and white has no choice but to surrender all six boxes. 
Chess – If white plays Qxg7, taking the pawn on S, that is checkmate. If they move Bc1 to the P, black takes the bishop with their rook, mating with Rxc1. 
Tic Tac Toe – White forms a line of three by covering the T in the middle line. If they instead select the T in the top line, grey takes the O in the bottom row and wins.
The letters from the winning moves spell out WORST, a reminder of the flavor text’s instruction to find the worst that can happen. The letters from the losing moves spell out INEPT, a fitting description of the losing moves in this puzzle.