Here's the explanation for the winning move in all the games. In some cases, there were multiple options but only one that fit the game and the crossword grid:
Battleship: To sink the final ship would be C4.
Chess: White puts black in checkmate with rook to A5
Connect 4: Slot #3 is a win for red (the clue implying it's red's turn)
Wordle: The word is TELLS
Trivial Pursuit: The answer is George II (the clue implying the 'History' category)
Scrabble: This one is tricky but the clue implies getting a 'bingo' which is using all letters in your possession. You can play DESSERTS down the left side to also make DEAR and SAP.