What system is this controller for?

Looks like a third party SNES controller.

First party ones look like this:

The port that it plugs into looks like this:

It's a "Blockbuster brand" SNES controller. They're apparently very rare. Unfortunately there doesn't seem to be much information online besides that.

(forum thread this came from)

(Ebay listing this came from)

I found the first link by searching "snes fighting controller" and the second (after finding the first) by searching "snes blockbuster controller"

This is a third party controller that - if I remember correctly - was designed for the SNES but also worked for the Sega Genesis (megadrive).

The switches in the middle were autofire cheats. If the switch was on, then the controller would automatically and repeatedly trigger the corresponding button, so you didn't have to hammer your controller.

Asciipad is a brand that does similar controllers:

https://www.amazon.com/Super-Nintendo-Turbo-Controller-AsciiPad/dp/B000W3ZDXO