Yeah, I'm going to disagree there.
Monogamy and polyamory can certainly be part of a person's identity (being wired to seek monogamous or poly relationships). However, for me, these terms are principally descriptors of relationship structures. They are parts of agreements between people who have relationships with each other.
In the case of a mono/poly relationship, there are two different relationships being described. When looking at all of the people attached to the relationship including metamours, it can certainly be described as poly. However, the nature of the relationship of the monogamous person to their partner can be described as monogamous from that person's POV if it doesn't involve anyone else for that person.
Again, I don't dispute that identity can play a part in this for many. But for me, the trouble is that when we tie too much of our identity into our relationship structures, it starts to create false divides between people and suggest more differences than there actually are.