Choosing a player is not targeting him. The Doll damaging the chosen player is also not targeting him. No targeting involved here at all, so hexproof doesn't help.
(Something targets only, if it uses the word "target", either in its text or in the rules for that keyword ability. Aura spells also target.)
I am both selfish and chaotic. I value self-gratification and control; I want to have things my way, preferably now. At best, I'm entertaining and surprising; at worst, I'm hedonistic and violent.