The API output for each user seems to be missing social links information. For example, https://www.drupal.org/api-d7/user/314031.json gives back a lot of information like websites, etc… but not social links. The information is present and can be seen on user profile page.
I am happy to try writing a patch if someone can point me to the correct project. I suspect we just have to update the definition to include this field.