Because Braddock tries to kill our hero (John Unger), he's a shoe-in for the role of antagonist. On top of that, he embodies the obsession with wealth that Fitzgerald satirizes in this story. Braddock thinks nothing of imprisoning or murdering the people who stand in his way, and he's exploited dozens of men (the most obvious example being his slaves) in the name of personal success.
When you look at "The Diamond as Big as the Ritz" as a parable rather than just as a story, you realize that the real antagonist isn't a specific character, but the idea being critiqued through satire. In other words, Braddock isn't the antagonist – the mindset and values which Braddock represents are. We're talking mainly about the insatiable desire for wealth, and the willingness to do jut about anything to get it.