The 'SPECIAL' refers to the non-standard milled opening, as I think others have alluded to. I've never seen any stubby-handled Williams SOE engineers wrenches, I don't recall seeing any on the Williams thread (we do have one, OP, see A-Z Index in Sticky at the top of the page), and I don't recall seeing a stubby SOE engineer's wrench, Superrench (alloy) or Superior (carbon steel), in any Williams catalog from 1912 to 1960. The SOE wrenches with a 1" milled opening are 9-1/4" OAL. The OAL's graduate more or less with milled opening size as you would expect. Notes accompanying those tables say Williams will put an offset of 45* or 90* in any order for an extra cost. I don't recall seeing a similar note offering shorter handles at extra cost. I could be mistaken. It's easy enough for someone to double-check me on IA/ITCL - they have a lot of Williams catalogs.
But I don't own any Williams SOE engineers' wrenches that are postwar (and RJ is definitely correct, that is postwar), and I have never seen any with model numbering scheme (BW-x) before. That could be key.
Not arguing that it's not factory, just saying there is no documentation I know of for Williams offering SOEs with short handles, standard or optional up through 1960, anyway.