have somebody do something vs. have somebody doing something

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.

Verb - clean

I have somebody cleaning the floor. (Someone is cleaning it right now.)

I will have somebody clean the floor. (Someone will clean it in the undetermined near future.)

I am having someone clean the floor. (Someone will clean the floor in the determined near future.)

I have somebody clean the floor. (Someone cleans the floor regularly for me.)

I have somebody doing the cleaning. (Someone is cleaning, but more than just a relatively quick job.)

I have somebody doing the cleaning of the floor. (Correct in formart, a bit quirky in style, and essentially means the same as the first example.)

Note: The last example would probably be used more with the word 'already' to emphasize that there is a whole complete task organized.

I already have somebody doing the cleaning of the floor.