When one reads about the "glum-faced" man, one thinks that he is the prisoner, and the well-dressed one is the officer. The officer, Mr. Easton, knows Miss Fairchild, another speaker, from their time spent in Washington social circles. The "glum-faced man" is also roughly built and shabbily dressed, thus playing into the stereotypical criminal.
One gets an idea that Mr. Easton went West and is working as a marshal, which Miss Fairchild finds fascinating as she's probably read a great deal about Western lawmen in the dime novels of the period. Mr. Easton claims that he is taking the criminal to Fort Leavenworth in order to serve a seven-year term for counterfeiting.
There is mention of this early in the story but it does not become apparent until the end of the story as the two men go to the smoking car. One of the passengers comments that Mr. Easton looked rather young to be in law enforcement.
Another passenger also noticed that usually a lawman does not have his right hand handcuffed to the prisoner. This only leaves to assumptions: Mr. Easton was left-handed; this was unlikely. The more likely scenario is that the rough-looking character was the lawman and Mr. Easton was going away to Fort Leavenworth to serve his sentence.
It is interesting that Mr. Easton was able to carry on a conversation with Miss Fairchild just like nothing important was happening and the Western lawman, the one who looked like the stereotypical villain in many stories, was actually the good guy in this short story.