The waterwheel analogy is apt.

You should, in fact, be able to build a very similar yo-yo device to replace a waterwheel, though it would likely be only drag powered, with no lift-generating mechanism. Makes me wonder if there is a yo-yo application for tidal generation, with the direction of the kite shifting with the currents.

There is a small company developing such a system where a friend of mine works as one of the innovators. The idea is to fly a hydrofoil ancored in the sea floor in a figure 8 almost exactly like the kite and extract the power by an attached water turbine. Unfortunately they got a useless web page. :-(