For me, "primitive" means using all-natural materials for the bow, glue, backing, finish, and string.
That was my answer, too. But then I got to thinking: Processed sinew, retted and combed linen fibers, and hide glue do not occur in nature.
To my mind, primitive archery just means shooting bows and arrows that are or could have been made in pre-industrial conditions. I have to hunt with steel points, and I use modern strings because linen is hard to find around here, and I stick my hand-stripped turkey feather fletches to my sitka spruce shafts with modern adhesives.
I classify myself as a sorta-almost-primitive archer.
I don't do many shoots or competitions, but I would think that self-bow, laminated wood/horn, laminated modern, compound, and crossbow would be reasonable categories. But around here, it's just fun to shoot with other people. I can shoot my self bow fine against other trad bows. If I compete against the wheely boys, I'm going to get whooped. That's a choice I make and I'm OK with it.