Eh, that's an untutored farmboy's opinion. Maybe he was actually pulling out his mind/consciousness/whatever goes to T'A'R and his lifeforce was coming with it, which would have the side effect of removing his soul from his body, as death does.
It's a type of energy that interacts with the world. That's not soul related.
<quotew>And of course, the connection to the OP is connected to the soul, meaning that Nynaeve(and everyone else that knows the weave) delved the soul of everyone whose connection to the OP she healed... Also, shields to block the OP go on the soul... And Warder bonds likely do as well. We don't know that it's connected through the soul. We know that the ability to channel is essential to a person beyond their physical qualities. That does not mean the connection to the Power is not physical. Channeling having physical effects on the channler in fact proves there IS a physical connection to the Power.

No evidence at all that it has anything to do with a soul. It would be an alien consciousness taking over Rand's body or place in the world if they won, but it was a physical struggle, not anything to do with a soul.
They never actually call it Soul, though. They call Air Wind, but spirit is always Spirit, because it deals with non-tangible things, like Tel'Aran'Rhiod, or psychic phenomena, like the warder bond. That doesn't mean they can do anything to that essense of a person, that lives on after their death and returns to the world in a new body. In my head cannon, Tel'Aran'Rhiod is just another level of physical existence, in which the Heroes have bodies and a dreamer manifests a body to go there. Getting stabbed in T'A'R does not affect your soul, it affects your physical body, through the link between the two.
That's my point. You can't do anything with it. Souls are utterly beyond the world or human action.
I don't think ripping souls out is quite what they say it is. For the idea of a soul to mean anything, it has to be above and beyond human interaction. I would say that in addition to the soul, there is a non-corporeal aspect of existence, which can manifest in the physical world in someways and interact with the physical, but is still just a construct, a kind of housing for the soul. This non-corporeal form would be what interacts through telepathy, it's what makes ghosts, it's what hangs around in the World of Dreams or what gets pulled into a Dreamwalker's constructed reality. It's what Machin Shin or Shadar Logoth attacks. It's what Ishamael & Asmodean tried to pull out of Rand. In a wolf, it's what gets eaten by Darkhounds, it's what gets taken by a Draghkar in a human. It's the underlying energy matrix that powers the body and makes it a person. In the Ogier who came out of the Ways, I would say that non-corporeal thing was gone or heavily muted, and left his soul unable to connect with his body. The soul is still there, because the body is still alive, but that non-corporeal layer is how the soul interacts with the body, and when that is all messed up, you die and your soul moves on along the Wheel the same as if it was your flesh and blood that was too badly messed up to continue biological functions.

Yeah, this could be all bullshit, but its how I reconcile my own belief in metaphysical existence with fiction which features ghosts and psychic phenomena and the use of souls. When you sell your soul to a demonic entity, you can't actually do that, so what you are actually giving up is a higher level of existence, that will almost certainly result in your damnation when THAT level ends and you go on to your eternal reward, but for it to mean anything, the only thing that effect THAT end is your own actions and mentality, your ability to align yourself in tune with a higher state of being, to sing along with the music of Iluvatar, for an example. If whether you go to heaven or hell is affected by the actions of a third party, heaven and hell don't mean anything. So they are pit stops along the way, for that spirit-body, that intermediate level beyond the physical, but which in genre fiction, really manifests and interacts with the physical.