An alternative theory is that the winglets are designed to "intercept" the vortex at an appropriate angle to produce thrust.

Consider a propeller spinning in a straight flow producing thrust. That's easy to understand because we see it all the time.

Now invert it so that a fixed foil is in a spinning flow. This is the case at the tip of a wing with a winglet attached.

The fluid wants to move from the high pressure side to the low pressure side which generates a vortex/twist in the flow. Put a small foil at a slight angle in the way of this twisting flow and you may be able to generate some thrust.