Nope. Those are IDC (Insulation Displacement Connectors) connectors. They don't have pins, they work by shoving the wires over a sharp blade-like terminal which penetrates the insulation. To replace it, you cut the connector off and use a punch-down tool to shove the freshly-trimmed wire onto the new connector. If you're really stuck on replacing it with the same type, you'll need something like this (example only, I'm not sure if that's the exact tool you'll need, I don't mess with IDC):
This video is for a network application, which is what IDC is generally used for, but the concept is the same, it should give you an idea of what you're after.
Really, though, the best thing to do is replace it with a Molex-style connector with Trifurcon pins. It's a better connection all around.
Hope this helps, and good luck with the Funhouse!