The problem is they also put "worms" in the same category, and they aren't designed by humans to do anything! Why is it that the natural laws of a worm responding to Earth's environment are distinct from the natural laws of Jupiter responding to the solar system's environment? I suppose because of complexity. But then why is a thermostat different from Jupiter despite being considerably simpler? I suppose because it was designed by humans and can be controlled. But then what about the worm, which is just as natural as Jupiter? "Thermostat" is especially problematic because a cheap thermostat is very simple to describe completely as a thermo-electric balance equation: it is certainly simpler to describe than an irregular ball rolling down an irregular hill. Yet apparently the thermostat is an agent and the ball is not.

The definition is just incoherent! "Sometimes an agent is deterministic and in this case the term only includes manmade tools, other times an agent is an apparently nondeterministic automaton and in this case we can include natural life." It only allows "agent" to be labelled ad hoc, and in particular blurs the distinction between "nondeterministic tool" and "lifeform" in ways that are scientifically unjustifiable. The only people this pointless word game benefits are liars like Sam Altman and Mustafa Suleyman; if people are well-intentioned then these definitions bring nothing but confusion.

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.