We can test the draw result by filling all the board's boxes:

@Test
public void whenAllBoxesAreFilledThenDraw() {
  ticTacToe.play(1, 1);
  ticTacToe.play(1, 2);
  ticTacToe.play(1, 3);
  ticTacToe.play(2, 1);
  ticTacToe.play(2, 3);
  ticTacToe.play(2, 2);
  ticTacToe.play(3, 1);
  ticTacToe.play(3, 3);
  String actual = ticTacToe.play(3, 2);
  assertEquals("The result is draw", actual);
}