They must intend to do what the Church does. If there is no intention as in a play then it is not baptism.
You must intend to DO what the Church DOES. That's why atheists can validly baptize. Apart from that, the details of the story are likely embellished somewhat and the account cannot be considered completely reliable. So whatever you want to make it of it, it's not proof of anything, poche. Try actually making a theological argument.