He was probably using it in a metophoric sense. Plenty of people call young boys "son" when they're not actually related at all. (Or in least in books they do
) Besides, Aragorn and Gandalf might have had sort of a father-son kind of relationship. Aragorn would always go to Gandalf for guidance and support, which is similar to what a son would do as well, I guess.
Or we could just say the people who made the tapes didn't know anything.