you can at most show that one of the player cannot have a winning strategy. It is not a constructive proof meaning it does not provide a perfect play strategy, so knowing that doesn't help. This is the so-call ultra-weak solution. The weak solution should provide an algorithm to secure a winner, or force draw against any possible move from the beginning. The strong solution is to provide an algorithm to win in any position. L. Victor Allis provided a weak solution of 15x15 gomoku in 1994. There wasn't a solution like that before.