Unlike Ganimes and Kameobas, Gezora is hinted by legends of the locals to have already been gigantic before coming under the control of  the space amoeba. Its cold powers do seem more on the supernatural end than the purely natural powers the other two kaiju, Perhaps from occupying Gezora the space parasite learned how to turn its hosts into kaiju, allowing it to create Kameobas and Ganimes.

On an unrelated note: I found this little tidbit while looking for a picture

Assistant special effects director Teruyoshi Nakano has openly expressed dissatisfaction with the names of Gezora, Ganimes, and Kamoebas, even rather jokingly suggesting “Gesoi” as a better name for Gezora, saying at a panel at G-Fest in 2004, “We made a mistake in naming those kaiju! One reason that [Space Amoeba] was not successful was because no one liked their names. Since Gezora is a big squid, it would have been better to call him Gesoi because that’s what people say when they order sushi! But then everyone would think you’re ordering sushi! So the names of the kaiju were bad” and “The names of these kaiju in Japanese are lousy. The names don’t fit, and the kaiju just aren’t scary. Maybe if we named the three differently, the movie would have been better. It was the names that killed the three kaiju.”