It's kinetic energy when it's actually in motion. It's potential energy while it's being stored.
Potential energy is specific to energy stored via it's relative
position in a system, due to some force field. This is most commonly gravity, in which the energy is related to the height of the object, but can also be in other force field like Electric or Magnetic, or microscopically within an object (the inter molecular forces of a compressed spring, for example). When released these can and usually do transform most of their energy into Kinetic energy as the field tries to return to a lower energy equilibrium state, though some can be lost in the form of heat , sound, etc.
The Rings charge by capturing the Kinetic Energy directly, somehow magically storing the momentum involved, and release it directly. They impart the energy into whatever objects are in the zone of fire, and that object finds itself moving without there being any of the normal other mechanism involved (yay Magic). Potential Energy isnt the only way to store or transmit Kinetic energy, it is just how it is usually done when you dont have magic to bypass the rules. It would be like assuming that Elaine's Lightning chain stores electricity through a chemical reaction, just because batteries are so common.
Also, in every description the rings are said to store "Kinetic Energy" from motion and emit a pure, magical Force effect. Saying they store Potential Energy is making an assumption on the "How" of it that we cannot be sure of.