Trevor, as well as many parts of the system, define "genderqueer" as "anyone who is queer in a way that influences their gender". This includes, among other demographics, GNC people and many gay people.
In particular, Trevor feels that gay men have an inherently different relationship to maleness and masculinity than straight men do. This is because so much of masculinity in society is defined by how men behave in romantic and sexual relationships with women. A man who does not participate in these relationships does not have access to the same kind of masculinity that men who do participate in relationships with women have.
Therefore, cis gay men undergo an experience akin to what trans men undergo, in which they have to question what their gender means to them and in which they often present that gender differently than they did before they knew they were queer. This is what Trevor is talking about when he describes himself as genderqueer.