When Blind Zealot deals combat damage to a player, its second ability will trigger. You choose a target for this ability when the ability goes on the stack. (It does not matter that the portion about choosing a target appears at the end of the ability. Targets are always chosen when a spell or ability is put on the stack.) At this point player can play other spells and abilities and respond to this triggered ability. Then when the ability resolves the controller of the Zealot chooses wether or not to sacrifice the Zealot. If the Zealot is sacrificed, the targeted creature is destroyed. Because this choice is made when the ability resolves, the controlled of the targeted creature does not know if you intend to ‘follow through’ and destroy the creature. In other words, if the controller of this creature wants to attempt to save his creature in some way, he will have to do that before this trigger resolves.