Based on the full range of what I've seen categorized as karambits, I'd say at a bare minimum, it must be of small to medium size with a hawkbill blade sharpened on the concave side of the curve. To this basic form you can add things like rings, sharpened bottom edges (the convex side of the curve), barbs, curb feelers or anything else you want.
Possibly anticipating your next question, yes, I do think knives like the Civilian, Matriarch, Harpy, Merlin, and the new Spyderhawk qualify as kerambits. To make the qualification even more pronounced, I would love to see Spyderco replace the standard steel spacer of the Harpy with an extended spacer that includes a ring. In my opinion, a ring on the butt end of the SPOT would also be cool and allow it to function much like a traditional karambit.