Given the problems we see in society, this definition is clearly not good enough for everyone and not good enough to satisfactorily deal with the problems arising; I might wonder what use a definition is if it doesn't actually guide us in solving problems. Perhaps this definition must be compromised when encountering reality in these situations.
Why do you need one? Why not just accept reality as it is - that reality simply doesn't match the simple, "everyone is a man or a woman" model? Sure, sometimes reality is just too complex to work with and we need to create a simplified model of it to work with, but this really isn't a complicated concept.
What are you talking about?
I'm talking about the wider problems caused by refusing to accept reality; gender segregated facilities, for example, that cater only to those who fit neatly into a binary definition. Problems caused by legislating, for example, that the only acceptable genders of record are "male" and "female", and in doing so excluding people who don't fit. Those kinds of problems.
If you'd like to exclude such people from your definition, and restrict it to people who are (for want of a better term) "stereotypical" male or female, that seems like a circular definition.