OK, eventually I found a solution. I write it below, whether somebody will need it. Basically, if in the download_artifacts method the local directory is an existing and accessible one in the DBFS, the process will work as expected.

import os 
# Consider you have the artifacts in "/dbfs/databricks/mlflow-tracking/<id>/<run_id>/artifacts/chain"

client = MlflowClient()
local_dir = "/dbfs/FileStore/mydir1" # existing and accessible DBFS folder
run_id = "<run_id>"
local_path = client.download_artifacts(run_id, "chain", local_dir)
print("Artifacts downloaded in: {}".format(local_path))

# expected output print message: Artifacts downloaded in: /dbfs/FileStore/mydir1/chain