In the part of the story that you quote for us, Fuzzy has found the doll but does not know of its significance. Black Riley does know that he could get money for the doll. This is the background to the passage that you have given.
There are two parts of the passage that must be explained. First, the part about the Romans and the Sabine. In Roman legends, there is an episode in which Roman men supposedly went and took wives from a neighboring community. You can find more about this episode in the link below (the Rape of the Sabine Women). So what O. Henry is saying here is that Black Riley wants to take the doll away by force.
Second, there is the phrase "merry-andrew." This is a phrase that is used to refer to a clown or a buffoon of some sort. So, by including this phrase, O. Henry is is showing that Black Riley looks down on Fuzzy and thinks that he is some sort of an idiot.