To have somebody do something most commonly means to cause somebody to do something (eg, ask, force, pay). But in this sentence the verb had means something like believed, perceived, recorded, claimed, or stated.
The clerk said the robber was tall and blond, but another witness had the robber as being of average height with red hair.
The history that the victors created claimed that the capitalists were the winners. More simply: The victors claimed that the capitalists were the winners. The rhetorical style suggests that the writer may be expressing disagreement with or doubt about that claim.
There are many reasons for chosing an -ing form over another type of word, sometimes more than one reason in a particular instance. Here, the primary purpose was to avoid the phrase to have somebody win, which suggests that have means cause. We would need more context to figure out if the -ing form is also related to a time aspect. I would guess not, as it probably functions here as a verbal noun instead of a present participle.