Without looking on the internet, I believe that in the days of tandem wheels and dual axles skates, Chicago brand was 'one of the good ones.'
I never had any strap-on your-shoe skates, but I robbed one of my younger sister's to make a skateboard, back in the early 1960's. It had narrow steel wheels. I used carriage bolts and a scrap of a 2x6 culled from one of the new houses being built in the neighborhood, to craft my first skateboard, which I put a painted design onto and shellacked. I wore those steel wheels down to the point they were like razor blades on their edges, we used to use baby oil on the bearings, which would get black oily residue all-over our clothes as we hiked back up our favorite hill for another 'go.'
I think Chicago was the brand in the 1960's that were shoes you'd rent at the local skate rink if you didn't have a pair of your own. When you gave the attendant your shoe size, he'd pull a pair out of the cubbyholes behind the counter, and give 'em a blast of Lysol, or some other disinfectant, before handing them to you.
On that tool, I'd guess the big open-end was for the truck to the shoe, and the box-end was for the axle.