When you create a new Snap*!* account, we ask for the month and year of your birth, and use that information (which never leaves your computer) to decide whether to ask for your email address or your parent's email address. I would recommend that practice.
If we were a business instead of a nonprofit, that wouldn't be good enough; we would have to verify that the alleged parent is an adult by, e.g., asking for a phone number and talking with them, or asking for a scan of their drivers license, or collecting a credit card number, etc.
We ask for an email address to be able to handle forgotten passwords, and also to notify users who are suspended for policy violations (although I don't think we've ever actually sent emails for that).
The paragraph quoted above from the Wix privacy policy about personal information from users of users seems to say that they collect such information only if their user asks them to. But I'd have to read the entire policy to know for sure.
But I also think it's right that every web site collects PII. More specifically, every web site that includes a Facebook thumbs-up button is sending everything your browser knows about you to Facebook automatically, whether or not you click the button. So I think wix is the least of your worries.