This is actually a complex question because there are complex inter-relationships between story elements and literary techniques Finney uses. The result of these inter-relationships is a multilayered presentation of conflict-theme-symbols. Let's see if I can briefly explain this complex interweaving of devices, but we'll use the literary term "theme" instead of the more colloquial "message" since they mean the same thing.
Starting with theme/message: Finney's theme is introduced with the minor conflict between Tom and Clare as the story opens. Their minor conflict is that they were to go to a movie that both wanted to see but, since Tom has "[g]ot to get this [work] done," Clare is going alone. Finney's theme is revealed as this tension between Tom's ambition and Tom's personal happiness. That Tom runs his hand through his hair tells us he is not being exactly honest about the work that has "got" to get done. This underscores the theme of ambition versus personal happiness. Though this conflict is a minor one, we can already see how conflict reveals theme, or "conveys message" in Finney's story.
Considering conflict: (conflict: battle or struggle with or against something): The major conflict is introduced when the "creased yellow sheet" on Tom's desk drifts out the window on hot air as the result of another minor (but significant) conflict between Tom and the apartment door. The conflict represents theme as ambition floats away from personal happiness. The narrator takes a long time developing and dramatizing the major conflict building tension and suspense up to the turning point when Tom takes decisive action to go out on the ledge. Tom's actions embody the theme of ambition versus personal happiness.
For many seconds he believed he was going to abandon the yellow sheet ... [then] he knew he was going out there in the darkness, after the yellow sheet ... On a sudden impulse, he got to his feet, walked to the front closet, and took out an old tweed jacket; ... He swung a leg over the sill...
Here we see that Tom's conflict precipitates action, and that action embodies abstract theme. Thus Finney uses conflict to convey theme through representational techniques whereby conflicts and actions represent abstract ideas.
Symbols: A dominant representational literary technique Finney uses is symbolism. There are many symbols and these symbols represent the conflict and the theme. Some complex symbols represent both theme and conflict. When these symbols drive the plot forward through conflict toward resolution, then Finney is using them to convey theme through conflict.
Some symbols are the yellow sheet and the window. The yellow sheet symbolizes Tom's thematic ambition. It also symbolizes Tom's conflict. It bears Tom's careful shorthand notations and has been carried everywhere he went, thus symbolizes his ambition. The window is a double symbol. It symbolizes Tom's warm personal life. It also dramatically symbolizes the divide between fierce ambition and personal happiness. When these symbols dramatize Tom's conflict ("he slowly ducked his head under [the window]"), then they simultaneously convey Finney's theme of ambition versus personal happiness, with ambition winning when he ducks under the window.