Adolescent pornography addiction requires early detection based on objective neurobiological biomarkers because self-report is prone to subjective bias due to social stigma. Conventional machine learning has not been able to model dynamic functional connectivity of the brain that fluctuates temporally during addictive stimulus exposure. This study proposes a state-of-the-art Dynamic Spatio-Temporal Graph Neural Network (DST-GNN) that integrates Phase Lag Index (PLI)-based Graph Attention Network (GAT) for spatial modeling and Bidirectional Gated Recurrent Unit (BiGRU) for temporal dynamics. The dataset consists of 14 adolescents (7 addicted, 7 healthy) with 19-channel EEG across 9 experimental conditions. Leave-One-Subject-Out Cross Validation (LOSO-CV) evaluation shows F1-Score of 71.00%$\pm$12.10% and recall of 85.71%, a 104% improvement compared to baseline. Ablation study confirms temporal contribution of 21% and PLI graph construction of 57%. Frontal-central regions (Fz, Cz, C3, C4) are identified as dominant biomarkers with Beta contribution of 58.9% and Hjorth of 31.2%, while Cz-T7 connectivity is consistent as a trait-level biomarker for objective screening.