The thing with Rapper swords is that they have one handle which twists to allow greater movement and the main body of the sword needs to be flexible as the dancers bend them into some ridiculous shapes. These days it is made with a very strong, flexible steel. Longsword is a bit less "bendy" by nature.
Looking at the slightly larger photograph, the swords do appear to have Rapper type handles. I'd go with Rapper rather than Longsword.
Our local side is hosting the annual Rapper sword dancing competition this year - Kendal will be awash with people in strange clothes and wielding bendy steel!