in 1958 world exhibition in Brussels Belgium, the main attraction of the american pavilion was a computer on which you could play tictactoe. Right in front of the american pavilion was standing the russian one where the main attraction was Sputnik.
Tictactoe is to my opinion a game that is just funny to program AI for. Then to test the AI by playing against the computer. Remember "Wargames" the movie. Tictactoe is "nerdy". Altough I can remember vaguely a 3D tictactoe which was composed of 3 grids of 3x3 supperposed, you could make three in a line on the X,Y or Z axis (or diagonals).
All this to say that I see two "ideas" to enhance your game. Either put some of "the history of tictactoe" to it, or transform the game into something less minimal. I like it minimal (but then really rough ala "wargames") but it could evolve along with levels...
And I don't understand why there isn't a mode against the computer. You miss all the fun of it! Programming the "AI" (not sure you can say its AI!).
The game has a good graphic layout and I experienced no bugs, it is fun for 30 seconds (been programming a tictactoe myself). I see no point of making a multiuser out of it, I can play this on messenger with the whiteboard and I will see my oponent, I can chat with him and send him some files and pictures while playing. And even all of this doesn't make tictactoe really enjoyable for more than a few seconds.
In the tictactoe I programmed (it is a small subgame) the aim is to let the computer win (for this in the AI one of the "rules" to win has been disbled so that you have deliberately to let it win) then the computer take control of the environment ...
for little stories read this also maybe some inspiration!
http://www.newscientist.com/news/news.jsp?id=ns99994063