Recent work in computational psycholinguistics has revealed intriguing parallels between attention mechanisms and human memory retrieval, focusing primarily on vanilla Transformers that operate on token-level representations. However, computational psycholinguistic research has also established that syntactic structures provide compelling explanations for human sentence processing that token-level factors cannot fully account for. In this paper, we investigate whether the attention mechanism of Transformer Grammar (TG), which uniquely operates on syntactic structures as representational units, can serve as a cognitive model of human memory retrieval, using Normalized Attention Entropy (NAE) as a linking hypothesis between models and humans. Our experiments demonstrate that TG's attention achieves superior predictive power for self-paced reading times compared to vanilla Transformer's, with further analyses revealing independent contributions from both models. These findings suggest that human sentence processing involves dual memory representations -- one based on syntactic structures and another on token sequences -- with attention serving as the general memory retrieval algorithm, while highlighting the importance of incorporating syntactic structures as representational units.