On some gas cooktops you won’t even be able to light the gas in the first place if you have no electricity (it would require using a match). Maybe if you are lucky though, once lit, if it stays alight, it will work without electricity.
You can theoretically use a gas fridge.
But my question was really a look at a future of no gas appliances, and a look at the whole house.
Your food is going off in the fridge, and you can’t cook it, and your hot water is not, and you can’t boil the jug and you can’t heat your house.
Electricity being a single point of failure would fail any kind of basic analysis. Maybe we need bio-gas.