What makes that argument extremely weak is analogies with contemporary obviously living animals.
For example, humans are not alive, because we get 100% of our vitamin D ascorbic acid by scavenging from the environment, along with a handful of other animals that presumably evolved in an extremely vitamin C rich environment. If any animal, including humans, ever evolve a new ability to internally synthesize vitamin C from glucose like every other animal, then given that there were non-synthesizer animals in their ancestry who we arbitrarily define as not-alive aka dead, then we could say that life evolved twice.
Note that humans could be defined as dead because we can't synthesize our own oxygen and have to scavenge 100% of it from the environment using lungs and so forth.
If you pencil whip the English language hard enough, anything with lungs or stomachs is not alive. A similar line of argument would lead to all saprophytes not being alive, which is pretty ridiculous. Wood eating mushrooms are not alive because they rely on the environment to provide all their wood dietary needs. Yeah OK whatever.