It is true that electric water heaters and induction cooktops will not be working in a power failure, unless the home has a battery backup system installed. However, gas appliances may not always work in a power failure. While most older models of gas stoves can be lit manually during a power outage, certain models of newer gas ranges are made with a safety feature called an interlock that prevents the burner from being manually lit. The purpose of an interlock is to prevent hazardous gas leaks by completely cutting off gas flow to the burners in the event of an electrical outage. To see if the stove is made with an interlock, check the owner's manual or manufacturer's website. Gas ovens require electricity to operate and cannot be manually ignited.
While gas water heaters do not use electricity as a fuel, sometimes an electric starter lights the pilot light. When this is the case, the gas water heater will not work in a power outage and cannot be re-lit with a match. Gas on-demand water heaters have a control panel that is powered by electricity, which will also not work in a power outage.