Computational drug repurposing aims to identify new indications for existing drugs by utilizing high-throughput data, often in the form of biomedical knowledge graphs. However, learning on biomedical knowledge graphs can be challenging due to the dominance of genes and a small number of drug and disease entities, resulting in less effective representations. To overcome this challenge, we propose a "semantic multi-layer guilt-by-association" approach that leverages the principle of guilt-by-association - "similar genes share similar functions", at the drug-gene-disease level. Using this approach, our model DREAMwalk: Drug Repurposing through Exploring Associations using Multi-layer random walk uses our semantic information-guided random walk to generate drug and disease-populated node sequences, allowing for effective mapping of both drugs and diseases in a unified embedding space. Compared to state-of-the-art link prediction models, our approach improves drug-disease association prediction accuracy by up to 16.8%. Moreover, exploration of the embedding space reveals a well-aligned harmony between biological and semantic contexts. We demonstrate the effectiveness of our approach through repurposing case studies for breast carcinoma and Alzheimer's disease, highlighting the potential of multi-layer guilt-by-association perspective for drug repurposing on biomedical knowledge graphs.