The simplest explanation is that when Langewiesche says "it will stall... out of level flight with cruising throttle", he is describing a situation where the aircraft is still banked, with insufficient power to maintain a constant airspeed, and the pilot is continually moving the stick or yoke further and further aft to maintain altitude, bringing the aircraft deeper and deeper into the "back side of the power curve".
Now let's consider some other possibilities.
While there's a lot of good information in "Stick and Rudder", there are also some flaws within.
For example, Langewiesche claims that in turning flight, sometimes it is better to center the slip-slid ball with an elevator input rather than a rudder input. I've never found this to be possible.
In general for a given position of the control stick or yoke, or for a given force exerted by the pilot on the control stick or yoke, an aircraft flies at a lower angle-of-attack in a steep turn than in wings-level flight. This is a consequence of the fact that a turn involves a pitch rotation rate, which creates an aerodynamic damping effect, which creates a pitch torque on the tail that decreases the wing's angle-of-attack.
If you set the throttle and elevator trim to maintain altitude and airspeed in a medium-banked or steep-banked turn, and you then you roll to wings-level without changing the throttle position and without pushing forward on the yoke, not only will the flight path curve upward, but the angle-of-attack will increase, and the aircraft very well may stall.
However, starting from a constant-altitude constant-airspeed steep turn, if you push the stick or yoke forward to avoid climbing as you roll to wings-level, and the aircraft had not yet reached the stall angle-of-attack in the turn, then the aircraft is not going to be at risk of stalling once it enters wings-level constant-altitude flight at the same throttle setting, even if there was a substantial loss of airspeed in the turn.
Things are a bit different if the airplane is allowed to descend at a very steep dive angle in the turn. A steep descent path does "unload" the wing to some degree, as drag rather than lift supports part of the aircraft weight. Still, it is hard to imagine that this effect would be strong enough to cause the aircraft to stall once the pilot reduces the bank angle to zero and attempts to maintain a constant altitude, as long as the pull-out from the descent is not too abrupt.
Note the reference to "cruise power" in Langewiesche's warning. Presumably this means that the throttle or power lever is fixed in a position appropriate for crusing flight. Langewiesche's warning appears to be aimed at a situation where the aircraft is rapidly losing airspeed in a steep turn and ends up deep on the "back side of the power curve", with the airspeed continuing to decay, as the pilot trades airspeed for altitude. Still, if we are talking about a substantial bank angle and the airspeed has not yet dropped to the (accelerated) stall speed, it is hard to imagine that once the airplane is rolled back to wings-level flight and the angle-of-attack is reduced, it will still be so deep in the "back side of the power curve" that it will not be able to accelerate while maintaining altitude, even with no increase in power setting. Perhaps in a really extreme case where aircraft was just about to stall before the pilot started to decrease the bank angle, the pilot might have to let the aircraft descend a bit first rather than trying to maintain altitude immediately upon reaching a wings-level attitude, to allow the airspeed to start to increase, especially in a jet where the "backside of the power curve" may extend further above stall speed than in an aircraft with a propeller, given that the thrust lever is assumed to be fixed at a cruise position.