The story
Evidently by metaphor with sticking (placing quickly, thrusting) something quite accurately into a specific place. The term is not specific to aviation: see stick. Thus, this term evidently does not come from a reference to an aircraft's stick (“control stick”). It also does not involve the same metaphor as deadstick landing, whose stick is, originally, a wooden propeller that has lost its engine power.
Etymology from Wiktionary, CC BY-SA 4.0.