MediaWiki (the actual Wikipedia website) runs on top of a traditional SQL database (originally just MySQL, but others are now supported too):

https://www.mediawiki.org/wiki/Manual:Installation_guide

There have been various forays into Semantic Web technologies. Previously people have done things like parse the infoboxes on Wikipedia pages and then import that into a triple store.

It seems that now the Wikimedia Foundation is finally interested in moving in this direction. But the software isn't there yet, certainly not at the scale Wikipedia needs.