The site started on MediaWiki. But, probably around 7 years ago, it switched over to a platform called DekiWiki, later renamed to MindTouch.
This is way over-simplifying it, but: MindTouch looks like a fork of MediaWiki (PHP) that's had all the database calls replaced by requests to a local web service running on .NET, with a Lua-based document scripting system (DekiScript) added on.
However, MDN ran all this on Linux servers - rather than Windows servers - so our installation was rather unusual. Eventually, the company behind the software decided to drop support for our kind of setup. So, we decided to move over to software we could support in-house, and launched it around June 2012.
What we have now started from the Django-based wiki that runs support.mozilla.org, called kitsune. From there, we worked on getting some practical feature parity with MindTouch. I added a node.js-based document scripting service (KumaScript) that mostly replaced DekiScript for our needs. We worked up some migration scripts, and moved the whole thing over.
It's admittedly kind of an evolutionary mess, at this point. But, at least it's our mess.