The case was about a government trying to restrict a sex offender from accessing web sites where he could engage in first amendment activities like commenting. The court ruled that they could not, absent a sufficient showing that the restrictions on the appellant's internet usage were necessary to prevent the sex offender from re-offending.

In fact the express language of the ruling states that social media sites are a means for accessing the public square, not that these sites are the public square. Moreover, these dicta statements (i.e., non-binding commentary) are a direct reference to the first amendment mall cases, which similarly involved activities that could occur in a public square. The mall cases held that private malls could ban speech because they were private facilities, thus they were not public squares even though the public could (and frequently did) engage in traditional public square activities in the mall.

TLDR: the private-public distinction matters for First Amendment law. The First Amendment only applies to public properties and public agencies, not private properties or persons.