That's how I read it. There's a similar statute for privately-owned airports that are open to the public.
There's the ambiguity. That "group" is not any sort of formal, or even informal-but-relatively consistent arrangement, and the "group" isn't operating the range ("operated by any...club, association, or group").
I'm not saying it couldn't be made to work, just that it's not plainly evident from the text that it would.
So....incorporate a group, eg "Oklahoma Weekend Shooters?" Or, operate it under an already-existent one (if the OP already has one)?