I think some gamers who want to use less electricity when gaming may buy a mini console which use less electricity than most full size consoles like the PS4, Xbox One, and full size desktop tower PC.
You could either just limit the amount of time you spend on video games, or play handhelds, as those would use even less electricity than a mini console, as they don’t have to be plugged into an outlet at all times, or use a tv/monitor.
I agree most gamers don't care about electric bills.
I think a low power mini game console which uses less electricity can be useful if you plan on installing a battery and battery powered screen on it to use during power outages or outdoors where there are no power outlets.
Consoles like the Xbox One and 360 can use a lot of power, so most cheaper batteries can't power them for many hours.