This issue was raised when the ad came out, and there is a distinct difference. The Dear Sophie account is not an account that is used by a child, it is one that is used by a child's father, and therefore allowed.
You would enter your own birthday. The Chrome ad is about an account used by a father to someday show his daughter, not creating an account for the daughter.
Actually that still doesn't work since you're supposed to only use your own real name in the Google account. It's against their policy to have a Google account in the name of someone else, even your kid, just so you don't have to put their real age.
Real names are only Google+ policy. In fact, I just checked, and a name isn't even required to have a Google Account. This is a bit of an edge case in that it is more of an account for a project than for a person, and Google doesn't really have it set up for this use (startup idea?). But it is the parent's account (they are entering the info, they write the emails from their perspective, input the pics/videos), so yes, the parent's birthday would be valid.
The real question is why did the OP even set up Google+ for an account intended to document their child's growth, and once they did, set it up as if the Google+ account was their child's.
