It assumes both players are as highly skilled as it is possible to be (e.g. they can see right to the bottom of the decision tree in every variation).
If the players are less skilled than this, i.e. they aren't going to play the best move every time, then any analysis you want to make about whether the starting position is a theoretical draw becomes moot because they aren't going to play the theoretical best moves anyway.
But if you assume the game is a theoretical draw from the starting position, then any game you lose is ultimately down to you playing at least one suboptimal move (otherwise you would have been able to force a draw), and any game you win is ultimately down to your opponent playing at least one suboptimal move (otherwise he would have been able to force a draw).
As it happens, I've just got home from playing a chess match in the local league. I lost, which means I made at least one suboptimal move, although I'm quite confident I made many!