All of those connections are custom made by the YouTuber Boojakascha. In the video, he shows how he made it. At 8:01 in the video, you can see that the bare metal bottom and back don't have the custom connectors.
If you ask me, all those connections are crazy overkill, but I don't own 15 types of lightguns that work with Time Crisis. The original unit is just a microswitch, super easy to interface with a ps1 pad or nearly any cheap usb gamepad, if you don't want to wire it directly to a keyboard encoder. Naturally, you could wire it all three ways if you want.
*Edit* Also, I would suggest that, if you haven't ordered already, you probably only need one pedal. There aren't really any Time Crisis games that are all that great with two player simultaneous play, unless you have two PS2's and two monitors, or I guess one very large monitor and a PC that can run Time Crisis 2 and 3 with the split screen mode at full speed.