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By your own logic you could argue that humans are just as natural as worms (and Jupiter). I don't know if you'd then extend that to include anything we build as well but even if you don't there's already a glaring issue - your criteria has resulted in the terminology being rather useless. It appears to include approximately everything or approximately nothing.

Similar logic can be used to argue that machines are no different from rocks.

At the end of the day it's an argument of semantics so it's always going to come down to some fairly arbitrary criteria. You could survey people to determine common usage. You could establish a standards body to define it. Probably some other options as well.

Recall that Pluto used to be considered a planet.

I think their apparent definition seems fairly reasonable, although it's far from the only one. It appears to amount to living organisms plus any machinations constructed by said organisms that respond to the environment in some clear manner. Thus worms, dogs, humans, and thermostats. Probably not bicycles or hammers. Drones probably only qualify when operating in an autonomous mode. I'm not seeing the issue.