Quoting from Fraser Cain at Universe.org, "...Astronomers think that between 9.3 and 13.5 Earth Masses is made up of these ices." You mention frozen gases, AKA ices. Therefore, we conclude that the gas giant similarity comes from an atmosphere containing mostly hydrogen and helium, with approximately one Earth mass. Another Earth mass of rock exists. We then find numerous Earth masses of methane, water, and ammonia ices. The majority of a giant outer planet is ice, therefore leading to the natural classification of an ice giant.