I used to have the 'Wordpress Download Monitor v3.3.5.6' installed and wanted to upgrade to the new 'Download Monitor v1.5.1'.
I deactivated the old version, deleted the download-monitor folder in the plugins directory and extracted the new version. In the backend I activated the new version of the plugin.
After that all my downloads seemed to be lost. I installed 'Download Monitor Legacy Importer v1.0.1' through the backend, activated it and followed your linked instructions:
simply go to Tools > Import and click “Download Monitor Legacy Importer”
It found all my old downloads and categories. I clicked the Import Now button and all my old stuff was successfully back there again.
I just can guess: but are you sure you installed and activated the 'Download Monitor Legacy Importer'?