This was probably a more difficult problem that what I had anticipated this to be. I got much fewer responses for this compared the previous ones. This puzzle combined two different concepts – Magic Square using numbers 1-9 and the tic-tac-toe game to arrive at the answer. Here is a link to the solution:
http://www.educreations.com/lesson/view/solution-to-puzzle-4/4805410/?s=hcOY81&ref=link
Hope you enjoyed this, and are looking forward to the next one, which is a relatively simpler one.
Alok Goyal's Puzzles Page 
Hi Chacha, i came up with a number matrix (magic square) which is mirror image of yours and I was using the same concept of ‘kaanta-zero’ game, however I was stuck trying to come up with a winning strategy. All I came up was how not to lose. I thought the puzzle asked for a winning strategy. Enjoyed this puzzle.
Another way to look at a solution or the best strategy without using the grid, is to see the sets 3 numbers between 1-9, you realize that 5 occurs the largest number of times in all such sets. Incidentally, the grid you drew also has 5 in the centre. The one picking up 5 remains most likely to win just as in ttt, the first mover marking the centre is the least likely to lose.
Agreed Ravi, but the thing is that even selecting 5 first does not guarantee a win. Similar to a tic-tac-toe, where someone selects the center, but still cannot guarantee a win unless the opponent commits a mistake.
Alok mentioned that the audience for this blog seems to be mostly IITians and their kids. For the moms and dads, here is a dissertation – http://www.austms.org.au/Gazette/2005/Jul05/mathellaneous.pdf
Note that translation of the problem from picking numbers to tic-tac-toe is not a proof that a winning strategy does not exist. This file provides the proof, and suggest many interesting variations.
Enjoy!
When I talked to my son, Sahil, about this game he mentioned that this also appears in the delightful book “Aha, Insight” (http://www.amazon.com/Aha-Insight-Martin-Gardner/dp/071671017X) by Martin Gardner.
Gardner gives this interesting isomorphic game. Quoting from the book..
It is played with these nine words:
HOT
TANK
TIED
FORM
HEAR
BRIM
WOES
WASP
SHIP
Two players take turns crossing out a word and initialing it. The first player who crosses out three words that have the same letter in common is the winner.