It actually might. If the Ring doorbell allows you to avoid opening your door just once or twice a week, the energy savings could exceed the environmental footprint.
A Ring doorbell has a 22Wh battery that lasts about a month or two per charge.
Having the door open for 10 seconds on a cold winter day can easily waste that much energy. About 10kW of heat loss for 10 seconds is 100kJ, higher than that 22Wh.
Likewise, the embodied energy of that 22Wh battery is about 22MJ, and might dominate the embodied energy of the Ring camera. So if it saves you from opening the door 200-300 times in its lifetime, that might be enough to pay for its own embodied emissions.
Plus not having to drive home to pick up a package, etc, etc.
Plus think of other smart devices like smart thermostats that might be part of the whole Ring system. Or perhaps if the Ring device prevents destruction of part of your home from theft.
I don’t even own a Ring doorbell, but I can see how it could actually help. Also, traditional doorbells aren’t that efficient. Especially if they have a little light.
Ring could also replace a window to see who is there, which is a big source of heat leakage.