"How would random sampling of incomplete data improve the results?"

It doesn't. The author means there is some actual population of shootings, and this dataset is a random sample of them. Since there are no systematic biases in the collection of the data, ie, it's not the case that the shooting of a black is more likely to be recorded than that of a white, the random sampling of the full set is sufficient. That's an assumption, of course, but given that assumption the rest works.

It doesn't improve the results, it just doesn't harm them.