When I think of kites, I always think of my dream of a kiteboat for long term cruising around the world.. purely kite powered, with maybe a small stabilizer sail if necessary.
My understanding is that there are a variety of advantages: the kite flies in cleaner air; the thrust from the kite is applied at one point, with less heeling moment than from a sail; the design of the boat is not constrained by the structural requirement of a mast
IIRC A kite powered boat called Jacobs Ladder held various sailing speed records at one point
I’ve a feeling that upwind performance would be lackluster. A modern Bermuda rig can be highly performant at all points of sail in a variety of conditions.
It works the same way, the kite acts like a wing and provides pull and something (kiteboard, fins, hydrofoil, etc.) resists that pull and provides a perpendicular force to the force from the kite power line.
"The rig consists of a triangular sail set aft of the mast with its head raised to the top of the mast; its luff runs down the mast and is normally attached to it for its entire length; its tack is attached at the base of the mast; its foot (in modern versions of the rig) controlled by a boom; and its clew attached to the aft end of the boom, which is controlled by its sheet."
If you're not familiar with sailing rigs, you probably don't even notice it as anything other than, "that's what most modern sailboats look like." This is precisely because it is a extremely efficient at sailing upwind. And their fastest speeds are roughly doing perpendicular to the wind.
Boats like you see in pirate movies and such have what is called square rig. These boats will sail their fastest downwind, but struggle much more in other directions.
EDIT: So I just realized that the Wikipedia article does not have a great explanation on the actual physics here. I'll do my best, though this is all subject to my (mis)understanding.
Obviously, just putting a sail on a raft with no other modifications will just push your raft downwind. You have some ability to control direction with the rudder, but that's it. To sail perpendicular, you need to start leveraging other forces. The main ones are lift force from the sail shape, and drag from the centerboard. [0]
Bermuda rigging uses a triangular sail that is rigged along the axis of travel. (Compare to square rig, where the sails are perpendicular to the axis of travel.) The sail has enough slack that, as wind fills it, it curves. The sails then begins acting as a vertically-oriented wing, using the airflow over the surface to generate lift -- though, in this case, the lift pushes the sailboat sideways.
So you have the wind attempting to push your boat sideways... That is not helpful for moving forward. Enter the centerboard, which resists this push by simply increasing the surface area of the boat under the water. In order to move sideways, the water has to be moved. So you have two opposing sideways forces, and the result is a bit like pushing a wedge -- the boat moves forward.
Also of interest in the physics is speed. So a boat sailing downwind can never go faster than some fraction of the wind speed. Because if it was, the apparent wind would either be zero or a headwind. However, a boat moving perpendicular or upwind can actually move faster than wind speed, because it is utilizing more forces than just the raw wind. And, in fact, the faster a boat moves upwind, the faster the apparent wind is, moving it yet faster.
Really small boats might get away without one. For example, a Hobie Cat (around 16 feet) is using a combination of its hull and a large rudder surface to achieve the same effects.
Wow. I couldn't get over how flat the thing sat in the water... no heeling at all. I guess that is a joint property of removing the mast (ie. reducing unnecessary vertical offset prior to thrust distribution across the hull) plus curved foils / mini-keels visible a the start and end of the video. Impressive stability given the low profile in the water.
Yeah, I'm curious why these are not more widespread. Maybe it's not as "cool" when it doesn't heel? And probably not possible to run in any regattas with that kite.