This story doesn't have a clear protagonist or antagonist. If the question is asking for a single protagonist, I don't think one can be provided with strong supporting evidence. That is because "The Machine That Won the War" presents three protagonists to readers: Swift, Henderson, and Jablonski. Each receives relatively equal page time and speaking parts. Additionally, each man plays an equal role in showing readers exactly how Multivac did not win the war. Together, these three men are the heroic figures of the plot, but no one except them will ever know that.
Finding an antagonist for this story is more difficult. There isn't a real, concrete "bad guy" who is fighting against Henderson, Swift, and Jablonski. I suppose a reader could argue the "Denebians" are the antagonists. We aren't sure if they are aliens or not, but the Denebian force is who is being fought against. I do not believe Multivac is a good choice for antagonist because the three men are not trying to undermine and destroy Multivac.
I believe that the best choice for antagonist is the abstract concept of being overdependent on technology. By the end of the story, the reader realizes Multivac was nothing more than a hulk of busted computing power. All three men used their own intuition to make war decisions based on the information being given to each of them. Multivac didn't win the war. Human decisions did. The story illustrates to readers that, as good as the technology may be, it still can't compete with human reasoning.