That site was a little confusing at first!
To be more precise:
- https://kiwix.org/en/applications/, scroll down to kiwix server.
- get a wikipedia dump in .zim format. AFAIU you can either get it from kiwix or get a database dump from wikipedia and convert it into .zim format.
- the rest, I’m guessing, is just running the server and pointing it to the .zim file.
edit: while that is probably the easiest option, the software wikipedia itself runs on is also FOSS: https://www.mediawiki.org/wiki/Special:MyLanguage/Download
Kiwix is probably the easiest / most readily available solution, but wikipedia runs on mediawiki which is also FOSS:
https://en.wikipedia.org/wiki/Mediawiki
https://www.mediawiki.org/wiki/Special:MyLanguage/Download
I’m guessing that most of the database download options provided by wikipedia itself should be compatible with a personal wikimedia installation:
https://en.m.wikipedia.org/wiki/Wikipedia:Database_download