He joined Google+ and _could_ optionally add a day of birth, because - well. You want your friends in a social network to post 'All the best' or whatever. So he provided this option freely, to share it with his circles of friends.
Not to link it to his main online identity. I don't think that it is obvious that there's a neat 'Hah! Another one entered his DOB in Google+ and is < 13, let's shut him out' trigger.
A human exhibiting this same behavior - peeking in his or her customers' windows to see if they're technically
violating terms of service in their private lives - would have been called a nosy busybody.
This is a major reason to avoid Google services. They are learning to better simulate a company that cares about privacy, but it's all still Big Brother at the back end.