Using the MediaWiki API
A great feature of a wiki based on the mediawiki software is the built-in API.
https://www.mediawiki.org/wiki/API:Main_page
This allows you to write programs that access data from any wiki that uses mediawiki, like wikipedia, or this one!
Getting the HTML of a wiki page
The documentation for the "PARSE" action of the API is here: https://www.mediawiki.org/wiki/API:Parsing_wikitext#GET_Request
Example link to get the HTML output of a page on THIS wiki in JSON format: