The term 'legal requirement' is used rather loosely by Google here. There are certain aspects of the services that they provide that are only available to over 13s, or over 18s or over 21s. I suspect that the main drive here is that they will be able to better target advertising when they know your age. They could just as easily have had you click 'agree' to a declaration that you are over a certain age limit.
Many security services will tell you not to share your birthday online as the combination of a name and birthday provides opportunities for identity theft and such. If you use a false birthday, it's somewhat risky as you may run afoul of the site's terms and conditions. I guess that one would be the lesser risk.