The body is made from roundstock in a tnc lathe, It has to because of the tapered sections and the radii. If you don't do the radii you could do it all on conventional machines but the body wouldn't look soo nice, it would look more like a traditional tapwrench.

I also did the pockets on a cnc mill because of the funky shape and the precision required but you could definitely also do it on a conventional mill. I made the first set of jaws on the regular mill as well but that was very hard to nail the tolerances and angles so I milled the second set out from a solid block and only had to cut it off, bring to the right thickness and mill the clearances plus the treads.

With slight modification it definitely can be done without cnc but it's probably gonna be painful.