Ys III uses character scrolling (or tile scrolling). It was very common on the MSX and Japaneses PC computers. They use sprites to overlay some of the hard edges to give them a better look. Otherwise there would be a lot more data to mess around with, or less detail. The game does run in mid res mode, so that makes the scrolling theoretically a little smoother than if it was in low res mode. But screen isn't actually scrolling. No scroll registers. It's just rebuilding the tilemap every frame. And since the tiles are 8 pixels wide, the game would move pretty damn fast if it were 60fps. I thought it was a noble effort considering this was a CD 2.0 game with limited ram for any type of dynamic tiles or such. Could be worse. Could be just as bland looking (exactly as it is) but with no parallax. For what it is, and once you get used to it, it's not bad. Strangely enough, there are a few parts in Ys III were they switch over to a normal scrolling routine and it looks smooth. I think that was a bad idea on there part. It just reminds you of how choppy the other areas are once you transition into them.
Ninja Gaiden on the other hand is just wrong. I don't know wtf they were thinking on that one.