I'd call it using a stick for a choke or a joint lock!
Seriously, absolutely it involves grappling, poor wording on my part, I suppose.
Splitting hairs, but for the sake of distillation down to basic elements, I'd factor out the stick in the definition, but then factor it back in as a "factor" that must be dealt with when grappling.
From my perspective, a military one, all of our grappling fights are fights over or involving weapons. So yes sticks, kubotans, ASPs become a player in grappling.
I guess IMM, the use of the stick still requires you to manipulate posture to gain control, that is unless you are using it as a blunt object to bludgeon.
Don't think I am making much sense...sorry it is late.