"I am fully aware that non-monogamy does not mean non-commitment, but for the sake of argument here, it is easier to assume it does."
Um...what? No it isn't! Maybe for the sake of proving your non-existent point it is 'easier to assume it does'. You cannot change facts just to make your opinion sound more worthwhile than someone else's.
"What you are saying is that some people can live in a primary relationship but have other relationships alongsdie that. yes?"
Yes, although not exclusively. There are as many ways to conduct relationships as there are people. Some non-monogamous people have a primary partner and then one or more other partners (sometimes termed as secondary, tertiary etc, but not often). Some have all sorts of relationships with all sorts of people without ever feeling the need to put them in some sort of heirarchy. Some are self-confessed 'sluts' who are single but sleep with several/many people on all sorts of terms. Some have several relationships all of equal importance and levels of commitment. Some live with several partners in the same house. And so on...
With the possible exception of some of the sluts, all of these types of relationship contain some form of commitment. That may be a commitment in the form of marriage (to one, obviously), or a mortgage, or children. Or it could be a commitment to spend every second Tuesday night together.