I believe that the question is using literary "context" and "period" interchangeably, so I will provide evidence to support Asimov's literary period and genre.
Isaac Asimov is a science fiction writer. New World Encyclopedia names Asimov's literary movement as the "Golden Age of Science Fiction." The dates of that period fit into the decade of the 1950s.
"The Machine That Won the War" definitely fits with science fiction. I'll go into some specific characteristics of science fiction and apply them to the story, but my favorite definition of science fiction comes from Orson Scott Card (an award winning sci-fi author).
“The difference between science fiction and fantasy … is simply this: science fiction has rivets and fantasy has trees.”
Basically, Star Wars and Lord of the Rings are the same type of story. One just has metal ships with lasers. The other has wooden ships with catapults.
Depending on your source, the number of characteristics of the genre may vary. I like using the following four characteristics from Eduplace.
• Science fiction is often based on scientific principles and technology.
• Science fiction may make predictions about life in the future.
• Science fiction often deals with aliens or with life on other worlds.
• Science fiction can comment on important issues in society.
Using those four characteristics, let's see how "The Machine That Won the War" fits the definition of science fiction.
The story is based on scientific principles and technology. The idea that exists throughout the story is that Multivac is an incredibly powerful computer that can analyze data better than humans; therefore, it can make better wartime decisions than humans can.
The story is also making a prediction about the emphasis that humans are and will be placing on technology and computers. Think about autonomous cars. Humans are already assuming that a computer-guided car is every bit as good at driving as a human.
Science fiction often deals with aliens. That is true, but I do not know if this Asimov story has aliens. All the reader knows is that the enemy force is known as the Denebians. That sounds alien to me.
The story also makes an important comment about technology. As the reader learns by the end of the story, Multivac was broken and was not making decisions. Humans were using their own intuition and making decisions based on that to win the war. The story is a warning against trusting machines and technology too much.