It's G+'s policy to prohibit under 13 G+ users, and Google's policy to handle G+ related policy the way they do.

From the linked act:

The primary goal of COPPA and the Rule is to place parents in control over what information is collected from their young children online. The Rule was designed to protect children under age 13 while accounting for the dynamic nature of the Internet. The Rule applies to operators of commercial websites and online services directed to children under 13 that collect, use, or disclose personal information from children, and operators of general audience websites or online services with actual knowledge that they are collecting, using, or disclosing personal information from children under 13. Operators covered by the Rule must:

1. Post a clear and comprehensive privacy policy on their website describing their information practices for children’s personal information;

2. Provide direct notice to parents and obtain verifiable parental consent, with limited exceptions, before collecting personal information from children;

3. Give parents the choice of consenting to the operator’s collection and internal use of a child’s information, but prohibiting the operator from disclosing that information to third parties;

4. Provide parents access to their child’s personal information to review and/or have the information deleted;

5. Give parents the opportunity to prevent further use or online collection of a child’s personal information;

6. Maintain the confidentiality, security, and integrity of information they collect from children.

I do think the commercial is ill-advised given their policy since it shows a use case, in an uplifting way, that they don't want to support.