I guess the piece I'm looking to replace is called a tread nosing (at least at home depot). I think you're right Henry, the moldings, though they are really low quality "wood" (something manufactured), are there to cover the ends of the risers. This builder just cut them into designs. I've seen this in some of my neighbors houses though the wood quality is better. Anyway the nosings have been notched (poorly) for this molding to go from one riser to the next.
Thanks for the help Henry. I think I'll go for it. Can hardly look worse than it does now?