Not entirely true. You can run a home bio digester in a sealed unit pretty cheaply. Feeding it compost and producing biogas (a mostly methane mix) at home that can be piped to appliances. Probably more upkeep than most people are up for. But if managed well, it can be a very ecological option. There are also ways this can be done at large scale with municipal organic waste.
That's not what's being discussed in the article, nor what's being connected in new home builds, nor what's being done at a large scale in NSW. So no, the gas supply being discussed isn't renewable.
It’s not just the emissions that comes from the stove directly. You need kilometers of gas pipes to service homes which can all form leaks or get punctured by eg road works.