You can see in the last link that there's also "კოსტავა, ბახტრიონი, დოლიძე, ხილიანის ქუჩის საუბნო განყოფილება", and these are just major streets in this district. The same would go with Kazbegi - it's not referred to as a neighborhood but as an avenue, just for administrative boundary naming purposes.