The article really doesn't put a good segue on this point so I can see why it seems jumbled. I'll give a shot at an explanation that will hopefully be a little clearer and more accurate

Butler approaches this problem of grievable life on the basis of performativity, not gender, but the approach has to do with their claim about how gender is maintained and produced as a system of classification of identities. Through a structure of repetitive acts that are socially established from many directions, some people are not really acknowledged as fully people, or as having the full value of humanity that allows their loss to be grievable. So the theory of performativity applies equally to how we view people as people (with all the ethical and axiological connotations this concept holds), and not just as man, woman, etc.