I offered that paper as background to someone who was incapable of offering a definition of gender identity. As I explain above, what transgenderists mean by 'gender identity' is slightly different, that they 'feel' they have an 'inner sense' of being a woman or a man. I think what the author describes in that piece as 'gender identity' has more in common with concepts of female or male socialisation than what transgenderists mean by 'gender identity'.
Note the definition in the Yogyakarta Principles is circular and in part based on stereotypes
http://yogyakartaprinciples.org/wp-content/uploads/2016/08/principles_en.pdf:
Gender identity is understood to refer to each person’s deeply felt internal and individual experience of gender, which may or may not correspond with the sex assigned at birth, including the personal sense of the body (which may involve, if freely chosen, modification of bodily appearance or function by medical, surgical or other means) and other expressions of gender, including dress, speech and mannerisms.