Polyamory doesn't mean people are disposable or interchangeable, and, while people do it, it doesn't mean that relationships outside the primary one are only sexual either, so, in the sense that your wife is talking about polyamory, no, it doesn't make sense that it's an excuse. What polyamory does seem to mean (among other things) is that one need not destroy one relationship to have another.
While it's understandable that the OP wants to feel in control of this situation, and he's right that this relationship is a threat to his current situation, it should be obvious that he has not been able to control his wife's or her friend's feelings. He won't be able to control those. The only thing he can control is his reaction to it. His wife has a second relationship. She is attempting to preserve the first relationship. All the OP can do is also attempt to preserve that first relationship.
I've been in this situation, too. In our case, the person in OP's role eventually destroyed the relationship by focusing on trying to control the other two rather than connecting with the original partner.
You don't have to be "everything" to your wife, but you have to be a partner she wants to connect to if you want to preserve your relationship. You're married, you have history, you are in a strong position. Focus on your strengths and the love you feel for your wife to calm your fears and process your anger. Of course, I don't know, and it's possible you can force your wife to end the other relationship, but from the looks of it, your wife is going down this road. My guess is you can't stop her, so you can choose to either go with her or watch her walk away. You may feel it's wrong or unfair, but it is what it is. You will be happier and stronger if you deal with what is, rather that what you think it should be.