Suppose you have a coin, which gives a random outcome X. But you can only observe the outcome of X when another independent binary random variable Y is true. How can you tell if X is biased? Since X and Y are independent, the observations where Y is false are irrelevant since they don't tell you anything about X. So you just keep the observations where Y is true, and from there you can apply a binomial statistical test to the observations of X.

[ In case you're wondering whether applying statistical tests to variable sample sizes is valid, the answer is yes: a p-value is a uniform random variable from the set of observables (augmented by a continuous random variable, since our set of observables is discrete) to [0,1]. Our p-value is a mixture of p-values on smaller sample sizes, so it is still uniform. ]

This is exactly what happens here: consider a random outcome {win,lose,draw}. If you don't have a draw, let Y be true and X be the outcome of the game. If you have a draw, let Y be false and X be a random coin with the same distribution as for non-drawn games. Then X and Y are independent random variables and the above applies.

Informally: draws are not useful information in determining whether there are more wins than losses.