I think it helps to think of there being two separate GAME OVER states, Player1Wins and Player2Wins. Then it is right to have two separate evaluations of game over.
Similarly there are two separate MOVES AVAILABLE evaluations, depending upon whose turn will be next.
|->Player 1 moves
| |
| P2 Moves Available -- no --> Player1Wins
| |
| yes
| \/
| Player 2 moves
| |
| P1 Moves available -- no --> Player2Wins
| |
|--yes