Probably much like with software designed from a description, there would be multiple solutions, all of which would meet the requirements given. Some would be better than others, some worse. Some would share common engineering designs, others would be completely unique.
And in the end if someone created a functional and usable tool for the job required (rotate pipes), who is to call those that don't accurately recreate the original wrong in their solution?
I realize by the way that the article is more about precision code like that description rather than writing code from the precision description. But still, there is still the concept that even precise things are open for interpretation.
This misses the key feature of a pipe wrench. The movable jaw has some swing such that it will tightly hold the pipe when moved in one direction, but will release the pipe when moved in the other direction. This provides the equivalent of a ratchet.
This is what distinguishes a pipe wrench from an ordinary adjustable wrench. It's that small amount of swing motion that gives it the ability to grab round things tightly. There are other forms of pipe wrenches which have a chain or a strap. They do not have a jaw adjustment nut but do have the ability to grab round things and a grab/release ratchet-like action.
The actual patent language (Stillson, 1869): "The lower part of the frame c extends forward of the shank A, and is recessed out, so as to permit said lower part to swing to the rear a sufficient distance only to bring said jaws nearly or quite parallel with each other." There's the swing part. Note another key part of the invention. The jaws won't close beyond parallel, so if you pull hard on the wrench, you rotate the pipe but don't crush it.
In the original patent, we see the "why", as well as the "what". The novelty of the invention is in the "why". This matters. If you made the tool described in the article, you'd have an adjustable wrench with teeth that would slip when you tried to tighten a pipe.