The story is unresolved. The viewpoint character, Michael Loomis, can't help looking at pretty girls even though his wife has complained about his roving eye and obviously feels hurt and threatened. A story does not necessarily have to have a resolution. Anton Chekhov has had a strong influence on short story writers, partly through demonstrating that a dramatic conflict can be left unresolved if there is no conceivable resolution. A noteworthy example is Chekhov's famous story "The Lady with a Pet Dog," in which the man and woman who have become entangled in an adulterous relationship are tormented by the fact that they feel they belong together but--by law, religion, society, economic realities, children, and geographical distance--are both irrevocably united in marriages to other people whom they despise.
Shaw's story seems like a confession--one that a lot of other married men might make if they were as candid as Michael Loomis. Men are psychologically programmed, hard-wired, to be attracted to women. They can't help looking--even though the look doesn't mean a whole lot and doesn't usually lead to anything more. He tells his wife that Manhattan is full of attractive, flirtatious, available women (which it is) and it is hard to ignore them. If he tries just sneaking peaks en passant he feels sneaky and unmanly. If he looks directly at them, as he would naturally do if he were unaccompanied, he hurts her feelings and spoils their time together.
It is a significant element of the story that Shaw's couple decide to have a drink and end up consuming three brandies each. It is the alcohol that brings out the truth. "In vino veritas." In Chekhov's day a marriage was nearly impossible to dissolve. In modern America nearly fifty percent of marriages end in divorce. It looks to the reader as though Michael and Frances Loomis are destined to be part of that fifty percent, but divorce may be a long way off or may never happen.
The humorist Dorthy Parker wrote a little nonsense rhyme which expresses a painful truth:
Men are polygamous.