This is one of Jimmy's choicest lines in the drama. It is a statement of how Jimmy and Alison's mother truly detest one another. He has nothing but contempt for her because she represents the class system that locks people like Jimmy out. She has disdain for Jimmy because she sees him as part of the rabble that would be unspeakable for her daughter. Essentially, both are diametrically opposed to one another.
Jimmy's invocation of the Knight code of honor in chivalry is both acidic and quite humorous. The code of chivalry demands that a knight look out for those who might not be able to look out for themselves. A knight, like Jimmy, would thus be required to look out for a woman like Alison's mother. Given how much he hates her, how much she fought against Alison choosing him, and how much resentment Jimmy has towards the stance that her mother took against him, the idea that both "took one look at each other" and recognized that "the age of chivalry was dead," is a reflection of how little both care for one another. It is a statement of how little Jimmy will go to help his mother- in- law. In a setting in which men were meant to act in chivalry towards women, Jimmy has no problem surrendering this code when it comes to his "Alison's mummy."