Exactly.

One of the best things about dwarf fortress is that playing it using that initially-confusing interface rather than shiny graphics is like doing math using symbols and equations rather than paragraphs and paragraphs of words.

Except the diagrams I saw didn't look like the other in-game circuits I saw. So, I'm still unsure if those are diagrams or in-game implementations. If you know, please tell me.

They're in-game inspired diagrams. The key is in the paragraph above the start of the 'Unclocked Logic' section.

     A
  →o * o→M O
   o * o
     B

The mechanical power goes in the first →, and the [M O] part is the output. A and B are the AND inputs. Gearboxes actually look like *, but o is also being used for gearboxes, albeit gearboxes that are just there to drain power.

The colored gif image at the top of the page is an in game implementation. The black and white characters are diagrams, but are quite accurate to what the game would show.

Those are not in-game implimentations. They might be diagrams of the linkages necessary to impliment it, though, but I can't understand them.

I get the impression that only some of the basic logic gates have been implemented yet, and that the rest is still theoretical.