Is a WiFi Gas Water Heater worth it?
One does not have to resort to an expensive internet capable device to enjoy the money savings of a controlled water heater. There are a number of mechanical electrical timers which would serve the intended purpose.

Prior to installing a solar water heater panel on the roof, our house was equipped with a water heater timer rated to 220v which had multiple trigger attachments for on and off. A large diameter clock dial to cover seven days provided the reference surface to which the triggers attached. 

An internet article suggests that this type of device can save money. I know from experience that it worked for us. Sporadic use of hot water in a small household gains the most, especially if you can block the times you need hot water and apply those to the timer disk.


Image courtesy of Home Depot.

I clearly have to read more thoroughly before answering!

Take a look at the site that obviously sells a specific product: 

Gas water heater timers!



It appears to serve as a gas flow control device. Under one hundred dollars US and there may be other manufacturers/dealers from which to choose.