Recently, Hyper-relational Knowledge Graphs (HKGs) have been proposed as an extension of traditional Knowledge Graphs (KGs) to better represent real-world facts with additional qualifiers. As a result, researchers have attempted to adapt classical Knowledge Graph Embedding (KGE) models for HKGs by designing extra qualifier processing modules. However, it remains unclear whether the superior performance of Hyper-relational KGE (HKGE) models arises from their base KGE model or the specially designed extension module. Hence, in this paper, we data-wise convert HKGs to KG format using three decomposition methods and then evaluate the performance of several classical KGE models on HKGs. Our results show that some KGE models achieve performance comparable to that of HKGE models. Upon further analysis, we find that the decomposition methods alter the original HKG topology and fail to fully preserve HKG information. Moreover, we observe that current HKGE models are either insufficient in capturing the graph's long-range dependency or struggle to integrate main-triple and qualifier information due to the information compression issue. To further justify our findings and offer a potential direction for future HKGE research, we propose the FormerGNN framework. This framework employs a qualifier integrator to preserve the original HKG topology, and a GNN-based graph encoder to capture the graph's long-range dependencies, followed by an improved approach for integrating main-triple and qualifier information to mitigate compression issues. Our experimental results demonstrate that FormerGNN outperforms existing HKGE models.