The pictured knife looks a lot like the model with a fire rod in the handle (Strike-a-light). That would lessen the need for matches. That pot looks very heavy, but it would certainly work for boiling water, hence scratch the water purifier. I would go for mirror, knife, tent, matches. My choices could vary depending upon the environment of the island - desert? rain forest? steppe?

This thread catches my attention because I am making plans to travel to an island whose population will vary from two to seven during my unfortunately all too short stay. I WILL pack a bit more....