Words have meaning on multiple levels.
On a technical level, yes, all humans are primates, but if the algorithm were following this rule, it would tag all humans in all photos as primates, but it didn’t do that. It only tagged black people.
That takes us to a social meaning level. In this context, you have to consider the long, racists history of dehumanizing black people. They have often been called “monkey” and “ape” with the intent to degrade and to segregate them from “people”.
In that light, and the fact that the label was not applied in all cases where appropriate, it is hard to see it as anything but racist. Probably not deliberately but if the training material contained racist material, it could bias the result. Even if the training material was inadvertently unbalanced and contained very few black faces, the algorithm would have less experience with black faces and would not know how to categorize them as well as white faces.
This is analogous to people who grow up and live largely isolated from close associates with those of other races. Their experiences are filled with varied samples of interactions with people of their own race, but are poor in samples with other races. In the case where we have less experience, we tend to fall back on broad stereotypes and our reactions show strong racial bias.