Surely its purpose is to prevent you pushing the rivet that little bit too far through the sideplate (we've all done it!) when you drive the rivet out; and similarly preventing you driving the rivet just a bit too far when turning the handle to push the rivet back in after repairing the chain; that is why it is adjustable - you can set it pretty accurately with no fear of over-driving the rivet.
I don't see how it could possibly "hold the chain in place" while you force the rivet out to break the chain. After all it shares the same axis as the rivet and the main screw with the handle. There has to be a space between the rivet and the end of the black screw...otherwise you wouldn't be able to force the rivet out of the roller at all; it wouldn't move a micron. The chain is held in place by the chain splitter's tooth which fits snugly between two adjacent rollers as it does on a sprocket or chainring.
The only other possibility is that the black screw is hollow.....in which case it could be used to hold the chain in place, but why would anyone want to do that as the tooth and/or a finger do that just fine?