First, welcome to Geekhack!
Just from the side angle pic, the switches look like
Key Tronic "foam-and-foil" switches, older type. They are capacitive.
There should be a circular foam pad at the bottom of each slider with a mylar sheet, and those foam pads tend to deteriorate over time. There should be replacement pads being available though, and some people have even made their own.
You should be able to unbolt the switch plate from the PCB and check. If you pull a keycap, the key's spring and slider should then fall out the bottom.
From the symbols on the keycaps, it looks like a kind of "ASCII keyboard". The ASCII character set was actually designed to map directly to a typewriter layout (that pre-dates ANSI) to make it easy to construct keyboards that produce ASCII character codes directly. ASCII keyboards were made as OEM products that would slot into all sorts of computing and telecommunications equipment. I believe it is likely that you should be able to read ASCII in parallel on the connector (but
how is another matter...).
This layout matches 1963 ASCII and (you can see that it is 1963 ASCII because of the up-arrow ↑ instead of the ^ character in later revisions).
However, USB does not use anything resembling ASCII, only raw codes of which keys are pressed.
So, if you did connect to the keyboard, your receiving microcontroller would have to interpret ASCII sequences and then send
fake presses to the host corresponding to what it
thinks the actual presses might have been, and that could be tricky. You would also be unable to send separate Shift and Ctrl presses, or map a key to a modifier such as Alt or Windows/Command.
But there might be another way that would go around ASCII altogether: replace the control circuitry with one of of xwhatsit's controllers for capacitive boards.
There is
a thread over on the Deskthority forum about using one for a Key Tronic board.