dead simple CLI tic tac toe game written in python 3

tictactoe.py

class TicTacToeGame:

    def __init__(self, player1=None, player2=None):
        # initialize an empty board
        # standard boards have dimension 3: 3 columns and 3 rows
        self.dimension = 3
        self._board = [None for n in range(self.dimension**2)]
        self.empty = "⬜"
        self.player1 = player1 or "❌"
        self.player2 = player2 or "⭕"
        self.turn = 0
        self.is_game_over = False
        self.winning_player = None

    def __str__(self):
        def formatSquare(squareValue: int) -> str:
            if squareValue is None:
                return self.empty
            elif squareValue == 1:
                return self.player1
            elif squareValue == 2:
                return self.player2
        rows = [self._board[i:i+self.dimension]
            for i in range(0, len(self._board), self.dimension)]
        return "\n".join("   ".join(map(formatSquare, row)) + "\n" for row in rows)

    @property
    def current_player(self) -> int:
        # player 1 goes on even turns and player 2 on odd turns
        return 1 if self.turn % 2 == 0 else 2

    def play(self):
        prompt = "Player {}: Pick a square to play (between 1 and 9) where the square numbers are increasing from top left across the rows and then down the columns \n"
        prompt = prompt.format(self.current_player)
        square_to_play = None
        while not square_to_play or square_to_play < 1 or square_to_play > 9 or self.is_occupied(square_to_play):
            square_to_play = input(prompt) or 0
            square_to_play = int(square_to_play)
        self.mark_square(square_to_play)
        if self.is_won_game():
            self.is_game_over = True
            self.winning_player = self.current_player
        self.turn += 1

    def is_occupied(self, square: int) -> bool:
        board_idx = square - 1  # square 1 is index 0 etc
        return self._board[board_idx] is not None

    def mark_square(self, square: int):
        board_idx = square - 1
        self._board[board_idx] = self.current_player

    @property
    def is_full_board(self) -> bool:
        return all([n is not None for n in self._board])

    @property
    def is_over(self) -> bool:
        return self.is_full_board or self.is_game_over

    def is_won_game(self) -> bool:
        horizontal_win_indices = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]
        vertical_win_indices = [[1, 4, 7], [2, 5, 8], [3, 6, 9]]
        diagonal_win_indices = [[1, 5, 9], [3, 5, 7]]
        for win in horizontal_win_indices + vertical_win_indices + diagonal_win_indices:
            vals = [self._board[i-1] for i in win]
            if all([x is not None and x == vals[0] for x in vals]):
                return True
        return False


if __name__ == "__main__":
    print("New game!")
    print("Time to choose your pieces")
    player1piece = str(input(
        "Player 1: Pick your piece. Use any emoji or letter. Or, just hit enter to use the default: ❌"))
    player2piece = str(input("Player 2: Pick your piece. Use any emoji or letter. Or, just hit enter to use the default: ⭕"))

    game = TicTacToeGame(player1=player1piece, player2=player2piece)
    print(game)
    while not game.is_over:
        game.play()
        print(game)
    if game.is_won_game():
        print("PLAYER {} WON".format(game.winning_player))