Based on his description, it doesn't have to have an interaction. But, if it doesn't interact with the material world at all, then there could be no connection or interaction at all between a body and a spirit. That means that you could not ever see or feel spirits in any capacity, and a physical human could not have a soul "attached" to it or associated with it in any way, even if the soul did exist.
If there were no interaction at all, it could never be detected and might as well not exist to us. If there were an interaction, you would expect to be able to detect evidence of it or at least one of its side-effects to indicate that something is there.
He is not saying that we're so awesome that we surely would see something if it was there, mind you. He's saying that what we can see already pretty well covers what is happening, so any other phenomena we want to say are happening are not detectable by any means yet devised and our world model works without the need for an outside unknown variable like spirits or souls to make the math add up.
Philosophically speaking, a phenomenon that is completely undetectable and does not influence or interact with anything in any way can be argued to be not happening, full stop. Things in this category fall into the realm of belief/faith, because that's the only realm things that can't be measured can exist in.
It didn't seem at all like an argument to me or an attempt by the OP to persuade anyone of anything. I read it as a description of their thought process as to how they arrived at the conclusions they did in their own life.
While some might find that enlightening if open to it or threatening if they disagree, it didn't strike me as an attempt to talk me into their (non)religion.