From this seminal publication, page 107:
“Since calculations of kite performance have resulted in Betz efficiencies of a few percentage points, the induced effects of the kite slowing the wind are assumed to be negligible in this paper”.
However a recent publication (among others) mentions page 4: “The present paper aims to provide a new theoretical perspective on the aerodynamic modelling and power limit of CKPSs by taking into account the effects of the induction factor.”
I think @dougselsam’ comparison between yoyo (said “lift” but in fact “drag-based” according to him) mode and drag-based Savonius-type device is particularly relevant: both are “pushed” (via reel-out tether downwind motion for the one) by the wind, and have a phase against the wind, unlike lift-based wind turbine or Makani-like device. And also the paper on https://www.sciencedirect.com/science/article/abs/pii/S0960148118304427 confirms that comparison in some way as "AWE drag power systems can harvest up to 16/27 of the power available in the wind " and "AWE lift power systems can harvest up to 4/27 of the power available in the wind ", “AWE lift power systems” being yoyo systems.
Loyd’s analysis and following papers study the efficiency by taking account of the kite area, while current wind energy considers the swept area within the actuator disc, the blade area (a.k.a. kite area) being only an element.
Little by little the traditional analysis elements for HAWT are gradually arriving in the field of AWE: Betz limit, Betz coefficient, actuator disc theory, induction factor…