What makes a rigid-heddle different from other looms?

The plastic healds themselves set this loom apart from others. Technically it is a frame loom, a class of looms where the weaving action happens within a frame. Other examples are pin or tapestry looms.

The rigid heddle is made from molded plastic pieces that are constructed in a slot hole configuration in various densities and widths. They are fixed between two wooden supports.

Warp yarns are threaded through each slot and hole. The yarns in the slots move freely and the yarns in the holes are fixed. When you lift the rigid heddle the yarns threaded in the holes are lifted above the yarns threaded in a slot. If you lower the rigid heddle then the hole yarns are pushed below the slot yarns. This action handily creates two sheds that are the basis of all plain weave weaving.

More complex looms such as floor and table looms have separate parts for a lot of the functions that a rigid heddle performs, but they are much more complicated to set up.