Kuraz the Light Monarch

Suppose I summon "Kuraz the light monarch" and my opponent activates "Trap Hole" or "Ring of destruction" in response (yes, I know the last one is Forbiden, but anyway). Can I still destroy up to 2 cards on the field?

since the summon hasn't been negated yes u can. Summon kuraz and activate his effect is Chain Link 1. Trap hole or Ring of destruction is activated and gets in chain link 2. At the resolve, Kuraz is destroyed and then chain link one resolves and kuraz's effect destroys 2 cards

George is right.

Kuraz will be able to destroy two cards and the owner(s) of the destroyed cards will draw cards equal to the number of their cards destroyed.