A dynamically weighted directed network (DWDN) is frequently encountered in various big data-related applications like a terminal interaction pattern analysis system (TIPAS) concerned in this study. It consists of large-scale dynamic interactions among numerous entities. Moreover, as the involved entities increase drastically, it becomes impossible to observe their full interactions at each time span, making a corresponding DWDN high-dimensional and incomplete. However, it contains vital knowledge regarding involved entities' behavior patterns. To extract such knowledge from DWDN, this paper proposes a novel Alternating direction method of multipliers (ADMM)-based Nonnegative Latent-factorization of Tensors (ANLT) model. It adopts two novel ideas: a) building a data density-oriented augmented Lagrangian function for efficiently handling a tensor's incompleteness and nonnegativity; and b) splitting an optimization task in each iteration into an elaborately designed subtask series where each one is solved based on the previously solved ones following the ADMM principle to achieve fast model convergence. Experimental results on two large-scale DWDNs from a real TIPAS demonstrate that the proposed ANLT model outperforms state-of-the-art models significantly in both computational efficiency and prediction accuracy when addressing missing link prediction on DWDW.