The word spirit has a wide variety of meanings in the bible. The word is basically used to describe any invisible phenomenon.
Personally, I think that the use of the word spirit when referring to the spirit in a living person or animal is widely misunderstood and there's two layers to the misunderstanding. First there is the misunderstanding that the spirit refers to some ethereal immortal personality that lives on after death. This I believe is false. But I believe that even the JWs' understanding of the term is also incorrect.
Spirit of life or the spirit in living animals and humans should be more properly understood as "breath". The same word translated "spirit" is used to refer to breath and wind. What separates living humans and animals from dead ones? Breathing. James' statement "As the body without spirit is dead" should be more properly understood as him actually saying "As the body without breath is dead" or "As the body that is not breathing is dead". Ancient people saw breathing as an identifying characteristic of living humans and animals. So in time figures of speech developed where they would refer to a person or animal that is alive as having "breath of life in the nostrils". This expression is just an idiomatic way of saying the person or animal is alive, by making reference to the trait that characterizes living beings - the fact that they're breathing. This expression is used in the flood account in Genesis.
When Genesis says that God blew the breath of life in Adam's nostrils, I believe it is speaking only literally. Perhaps the author of Genesis knew that newborn babies often had to be made to cry to initiate their breathing. The author could have wondered how he will get around this issue in writing about a grown man made from the dust who has to breathe to live but can't breathe before he is alive. It would not seem dignified or proper for God to smack him on his behind like is often done with newborns. But even then newborns are already alive and can start breathing by crying in response to pain. But Adam was not even alive to start crying even if God smacked him on the behind. The only way around this logical conundrum is for the author to say God started his breathing for him by breathing into his nostrils. The author was actually trying to overcome an issue that would have caused some to wonder. JWs are simply overthinking the statement. It has nothing to do with any mysterious life force being planted into Adam. Just as there is no immortal spirit person within us, neither is there any mysterious life force keeping us alive. JWs are reading too much into a figure of speech that has references to literal breathing.
All expressions that refer to spirit in the context of being alive and dying are simply literal references to breath and breathing, being used to refer to being alive or dying. When the bible says a man's spirit goes out and he goes back to his ground what it is actually saying is that his breathing stops and he goes back to his ground. Spirit = breath. Why the expression "spirit/breath GOES OUT"? Because when a person dies his last breathing action is an exhalation as the diaphragm relaxes.
Ancient people knew little about biology and the science behind breathing. All they knew is that it was essential to life and that stopping it meant death. When a person made his last exhalation at death, they saw that his breathing stopped as the breath seemingly left his body in his last exhalation. From that the idiomatic expression of "breath going out" at death could have been born. But because the same word for breath is also used for miraculous spirit like angels and holy spirit, the word breath gets lost in translation as "spirit [ethereal immortal personality or invisible lifeforce] going out".
There is no invisible lifeforce. The ancients were simply using idiomatic expressions related to life-sustaining breathing when referring to being alive and dying. It's as simple as that. Watchtower is reading too much into a Hebrew idiomatic expression by translating what should be "breath" as "spirit".
That's my 2 cents opinion, anyway.