So..... is a "check nut wrench" an actual thing?
It was, especially in the late 1910's and early 1920's, when your wrench was made (by J.H. Williams, either in their Brooklyn or Buffalo factories - can't see the logo close enough to tell), for check, jam, or lock nuts, as others have alluded to, on all kinds of machines, including engines with valves and tappets, I believe.
Single or double open end wrenches in this era and well up through the 50's had very specific names for very specific applications, such as set screw, tool post, machine, textile, water pump, service, and engineer's wrenches. These all had different milled opening size ranges, profiles, head angles, and shanks/handles for different applications.
Not all of them had their functional name forged-in, and this exotic practice did not last long even for the check nut wrenches.
The closest thing to today's standard DOE wrenches would be the engineer's wrenches, which had milled openings for the entire range of what we think of as "standard" nuts and bolts (in fact, up until the late 50's there were
two major standards - U.S.S. and S.A.E.), and hex cap screws.
Not to sound like a pedant, if you're going to collect old wrenches, even sporadically, as a part-time hobby, I highly recommend leafing through a vintage catalog (1920-1950). Everything I summarized above will become apparent within a dozen pages. Any of the early giants who catered to different industries (machines shops, textile mills, automotive, etc) will do, but you really can't go wrong with the company who made the wrench you just found.
Nice find, by the way!
EDIT: Unlike Alloy Artifacts, the Tool Archives, established by esteemed GJ member twertsy, and populated with information and examples posted by him and other GJ and broader (Garage Gazette, etc) tool collecting community contributors, has an open library. Once you register, which is free, click
here for the Williams section.