A friendship between an adult (40+) and a child (14-16) who is unrelated. Similar interests include gaming, sci-fi, general geekyness. Interactions include Facebook, Tumblr, Twitter, Gaming night (with child's parent participation).
Is it normal for an adult to be friends with someone so much younger?
Is it normal for an adult to be friends with someone so much younger?

As long as the friendship maintains a respectful barrier then it should be OK. You should also make sure the child's parents are part of this friendship too since they will have the final say in "yes" or "no"