Well I most often think of anything cooked on a BBQ
is .... ta da! BBQ'd!
a method/style of cooking.
and I guess (to me) a BBQ is a hibatchi, free standing gas or coal grill, be it kettle or whatever
shape! It also needs to be used outdoors. Brick and block built ones included. Excuded are campfires, with a fire grate positioned over them, or tripod. That's just camping.
Then there are the sauces made specifically to glob/glop/drown on BBQ'd foods and carry the name of BBQ in them somewhere. (think they were created simply to cover up burnt foods and try and rescue
to make them taste a little better)
Ham is smoked pork, originally hung in the house chimney, so the purist might have a problem with that.