i think i found the short story you’re referring to. what you’ve quoted is from the summary of the story. though in my opinion it reads more like a teaser. the genre is horror or suspense. (technically the summary says it’s horror but to me the story reads more like suspense with a good dash of horror.)
the teaser is from the two sentence fragments you’re unsure about.
男の目的は何か？ seems to be pregnant with much possibility. what did the man have in mind? what was his plan of action? there’s much that can be read into these vague words. i’m not very good at translating, but i would render this first fragment along the lines of “did this man have some kind of objective?” but i’m already reading too much into it.
駅の待合室で男が語る物語は？ seems easier to understand but i had to start reading the story to make much sense of it just because i couldn’t make a connection between the two fragments—they’re just very incongruous next to each other. “what was the story the man told in the station waiting room?” but again i’m reading a lot into this.
both these sentences are cliff hangers meant to grab you. i don’t think a native japanese would really be able tell you definitively how to finish those fragments. they’re meant to grab you and make you ask, “what’s going on here?”
just the juxtaposition of a man suddenly appearing with a gun from the train that should not have returned and then the almost benign sounding second teaser about someone telling a story makes you wonder what could be going on here.
and truly the story does start off very horrifically.