Answering to a comment which seems to be closer to the core of the issue here:
In every game, if people play a perfect game they win and they lose otherwise. What is the utility of the theorem then, please?
The theorem allows you to classify games. Assuming all players play perfectly, there are games where the beginning perfect player will always win, others where the player to make the second move will always win, and still others where any tournament between perfect players will lead to a draw. So it says that you can classify (deterministic finite perfect-information two-player) games into these three categories.
As others have already stated, perfect players for chess are hard to come by, so at the moment (and for the forseeable future) we don't know which of these categories chess falls into. But we do know – thanks to the theorem – that it must fall into one of the categories.
The relevance of this finding for actual chess players is zero. The relevance for game theorists is a bit larger, but obviously the theorem is most useful in those cases where you can actually determine (in reasonable time) which of the three cases holds, like e.g. Tic Tac Toe. Once you have analyzed a gaim sufficiently to know the perfect strategy, and are able to remember that strategy (as Voo pointed out), then the game will likely become boring. That's the reason why there are no world championships for standard Tic Tac Toe: all games would be draws, since it falls into the “both players can force at least a draw” category. For some other games, perfect strategies are known as well, and more might join that club eventually.
Come to think of it, there might be one possible application of Zermelo's theorem for chess players: blaming frustration after a lost game on the game design. “I did play perfectly, but unfortunately so did my opponent, and the game is designed in such a way that I had to loose it.” A claim which is hard to believe but also not easy to refute. The part about the game being designed in such and such way is this classification I've mentioned, which is unknown so far. So you'd have to show that the speaker did make some suboptimal move at some point. (If his opponent did make a suboptimal move, and the speaker lost anyway, that means the speaker must have made such a move as well.)