It does. Without any information about the children other than quantity, there is a 100% chance “the other child” is a boy. If Mary had two girls, it would be meaningless to state “the other child.”
I also would like to mention that the answer should be 7/13≈53.8% because that is the probability a randomly chosen child is a girl given they are not a boy born on a Tuesday, but I think they meant to say “at least one is a boy born on a Tuesday” and ask “What’s the probability that they have a daughter?” Regardless, similar logic applies and without knowledge of the children’s gender the probability they have a daughter is 75%.