Some of the older coaster brake hubs had a notched lock ring that held the gear on to the driver instead of the circlip we see on almost every hub made since 1960. Some old coaster brakes had a notched round "nut" that held the brake arm on. I think the tool was mostly for working on the hubs. The wrench sizes are probably the same as axle nuts. 11/16" or 5/8".
Part of a three-piece set, each of which sport the same peculiar notch.
It doesn't look like that would get a very good purchase on a lockring, though I can't dismiss that possibility. Every function is listed on the package...except that notch! Go figure.