This paper proposes an adaptive neural event-triggered output-feedback optimal tracking control scheme for uncertain discrete-time pure-feedback nonlinear systems. The scheme addresses the challenges of immeasurable states, nonaffine terms, and network resource constraints. A neural network (NN) state observer is designed to estimate the immeasurable system states in real time. The implicit function theorem and mean value theorem are combined to handle nonaffine terms, while the variable substitution approach is used to overcome the causal contradiction problem during backstepping design and avoid n-step time delays. An adaptive critic design framework is employed to design an optimal controller, with critic and action NNs used to minimize the system's long-term performance measure. An event-triggered (ET) mechanism is embedded between sensors and controllers to reduce network burden, with a novel ET condition developed to save network resources and ensure desired tracking performance. The proposed scheme guarantees that all closed-loop system signals are uniformly ultimately bounded (UUB). The main contributions include the design of a neural state observer to estimate immeasurable states, the use of the variable substitution approach to overcome causal contradictions, and the development of an ET condition to reduce network resource usage. The scheme is validated through simulation, demonstrating its effectiveness in achieving optimal tracking control for uncertain discrete-time pure-feedback nonlinear systems.This paper proposes an adaptive neural event-triggered output-feedback optimal tracking control scheme for uncertain discrete-time pure-feedback nonlinear systems. The scheme addresses the challenges of immeasurable states, nonaffine terms, and network resource constraints. A neural network (NN) state observer is designed to estimate the immeasurable system states in real time. The implicit function theorem and mean value theorem are combined to handle nonaffine terms, while the variable substitution approach is used to overcome the causal contradiction problem during backstepping design and avoid n-step time delays. An adaptive critic design framework is employed to design an optimal controller, with critic and action NNs used to minimize the system's long-term performance measure. An event-triggered (ET) mechanism is embedded between sensors and controllers to reduce network burden, with a novel ET condition developed to save network resources and ensure desired tracking performance. The proposed scheme guarantees that all closed-loop system signals are uniformly ultimately bounded (UUB). The main contributions include the design of a neural state observer to estimate immeasurable states, the use of the variable substitution approach to overcome causal contradictions, and the development of an ET condition to reduce network resource usage. The scheme is validated through simulation, demonstrating its effectiveness in achieving optimal tracking control for uncertain discrete-time pure-feedback nonlinear systems.