It had some slight blemishes, left overs, not updated comments. I fixed those and put the object style according to vegaseats style (but kept the import * from wooeee)

I ran it through pep8 checker to clean up last irregularities in style.

from __future__ import print_function

try:
    from Tkinter import *
except ImportError:
    from tkinter import *

from functools import partial


# vegaseat inheritted from Tk object
class TicTacToe(Tk):
    def __init__(self):
        Tk.__init__(self)
        # pointer to buttons and StringVar()
        self.button_dic = {}
        self.title('Buttons TicTacToe Test')
        self.geometry('400x500+0+0')
        self.top_frame = Frame(self, width=400, height=500)
        # True = "X", False = "O"
        self.player = True
        self.buttons()
        Button(self.top_frame, text='Restart', font=("Helvetica", 16),
             command=self.restart).pack(side=BOTTOM, expand=True)
        self.announce = StringVar()
        Label(self.top_frame,
              textvar=self.announce,
              font=("Helvetica", 16)).pack(side=BOTTOM, expand=True)
        self.clear_dict()

    def clear_dict(self):
        """ clearing the texts in buttons and list of moves """
        # list of "X" and "O" moves
        self.x_o_dict = {"X": [], "O": []}
        for ind in range(1, 10):
            self.button_dic[ind].set(str(ind))

    def restart(self):
        self.player = True
        self.announce.set("Restarted. X's turn")
        self.clear_dict()

    def buttons(self):
        """ create 9 buttons, a 3x3 grid """
        for j in range(3):
            f = Frame(self.top_frame)
            for i in range(3):
                ind = j * 3 + i + 1
                self.button_dic[ind] = StringVar()
                self.button_dic[ind].set(str(ind))
                b = Button(f, textvariable=self.button_dic[ind],
                           font=("Helvetica", 16),
                          command=partial(self.cb_handler, ind))
                b.pack(side=LEFT, expand=True, fill='both')
            f.pack(expand=True, fill='both')
        self.top_frame.pack(expand=True, fill='both')

    def cb_handler(self, square_number):
        """ Set button to symbol if not clicked before,
            announce result in announce label.

        """

        player = "X" if self.player else "O"

        if (square_number not in self.x_o_dict["X"] and
            square_number not in self.x_o_dict["O"]):

            self.button_dic[square_number].set(player)
            self.x_o_dict[player].append(square_number)
            if self.check_for_winner(player):
                self.announce.set('%s is the * Winner *' % player)
            elif sum(len(self.x_o_dict[item]) for item in self.x_o_dict) == 9:
                self.announce.set('** Game was draw **')
            else:
                self.player = not self.player
                player = "X" if self.player else "O"
                self.announce.set("%s's turn" % player)
                return
            self.clear_dict()
        else:
            self.announce.set("Occupied, pick another")

    def check_for_winner(self, player):

        winner_list = [[1, 2, 3], [4, 5, 6], [7, 8, 9],
                        [1, 4, 7], [2, 5, 8], [3, 6, 9],
                         [1, 5, 9], [3, 5, 7]]

        set_in = set(self.x_o_dict[player])
        for winner in winner_list:
            if set(winner).issubset(set_in):
                return True

if __name__ == '__main__':
    bt = TicTacToe()
    bt.mainloop()