Yes, Chuck, that's the electrosocket.
I can't speak for the futuristic Klein, but on the Tele it CAN be installed with the part on the right of my pic left in place. If you do, it will look much like the image you've posted-- the threads of the jack "buried" in the electrosocket, and most right-angle plugs will "eject" themselves.
However, if you REMOVE the stock part entirely (including the part to the right in my pic), it will work much better, and will be compatible with most right-angle plugs. Below is an image from my 1974 Tele Thinline, with electrosocket installed. It didn't always look like that-- BEFORE I had removed the toothed spacer embedded in the wood of the stock guitar, it looked almost exactly like yours.
But I got frustrated one day, went in and tapped that part out, and now you can see that the standard Switchcraft #11 jack protrudes nicely, sticking out enough to allow the standard right-angle plug plenty of purchase.