Of course a game of chess could in theory go on forever, but eventually you would wind up with a board configuration back that was identical to that you found yourself in earlier in the game. Assuming both players have are using the extended form of the game as their strategic guide, that game is a draw, because they will just keep going forever, endlessly repeating itself.
Zermelo's theorem really shows that, assuming each player knows the extended form of the game and makes no mistakes, one player either has an insurmountable advantage over the other or both players will always either draw or keep playing forever.
Let's say that computers calculated it out and the second-mover had that advantage. If Player 2 had the extended form memorized or available, then he/she/it could never lose the game. The best player 1 could ever get would be a draw or a game that never ends, and at worst he loses. There would be no ploy or gambit that Player 1 could devise that player 2 could not negate. On the other hand, player 2 might have winning strategies, but could never do worse than a draw.