The reason it is not working is that download is being corrupted during the download process by either MS Edge or Windows Defender. I just download the program using Google Chrome and had no issue with download. This issue is related to Windows Defender and other antivirus software and how they protect Windows.
I wish that was really the problem, but unfortunately it isn't. My download was not corrupted - it passed the CRC32 check: 93FEB31F.
Regardless of what browser I use to download the installation file, e-Sword 13 will not start on my PC after a clean installation.
My only guess is that it's something similar to the problems some had with the first release of version 12.x, which required an update later to fix the issue.