Well OK I will concede that nobody owns language, so someone is fully at liberty to use the word 'gender' to mean anything they want. However, unless people are purposely trying to confuse the issue, the generally agreed modern definition is that gender is the cultural concept i.e. the presentation. In the UK you can get a gender recognition certificate; it is therefore clear that this is also the legal definition.
From the World Health Organization website:
"Gender refers to the characteristics of women, men, girls and boys that are socially constructed. This includes norms, behaviours and roles associated with being a woman, man, girl or boy, as well as relationships with each other. As a social construct, gender varies from society to society and can change over time."
The OED has similar definitions (although you have to wade past all the uses of gender in language first) e.g.
"Psychology and Sociology (originally U.S.). The state of being male or female as expressed by social or cultural distinctions and differences, rather than biological ones; the collective attributes or traits associated with a particular sex, or determined as a result of one's sex. Also: a (male or female) group characterized in this way."
If you choose not to use gender in its cultural form (which is of course anyone's right), then you can quite happily spend all your time talking about how confused it all is, but that's mostly because you've chosen to use confused, non-standard definitions...