Use the browser that you use now to post: you are able to download because cookies are enable and you did login. So if java-script is also allowed then can you download books from this website. The book module must be in your download folder if you successful downloaded it.
Now move the book module from the download folder into the e-Sword folder.
You did not give info about the e-Sword version and OS that you use so it is harder for me to help. Nor did you post a link to the module that you want as example.
The default e-Sword folder for the Windows versions are:
C:\Program Files (x86)\e-Sword
Or
C:\Program Files\e-Sword
Then start e-Sword (e-Sword read automatic al the modules in the e-Sword folder).
double clicking is useless.
(In the windows editions of e-Sword)
For topic or reference books need you to click on the "icon with the books" near B,C D, E and "the sun and mountain" icons.
The modules made for e-Sword 7 and 8 are not supported in newer editions so you need to convert it to e-Sword 9 or 10 modules.