As for Matrix, I’m not personally familiar with it but a quick look up suggests it’s a protocol so by my offered explanation, the answer is no.
In my view, we’re talking about a term which is in general usage in the mainstream media.
It means things like Facebook and Twitter, but obviously others like Instagram, Gab, etc.
These all seem to enable public discourse of one kind or another.
Private 1-1 messaging platforms and merely social features - e.g. an Apple Music family plan, seem to have very little to do with this.
Just because a feature involves more than one user, it doesn’t become a ‘social network’.
As for Matrix, I’m not personally familiar with it but a quick look up suggests it’s a protocol so by my offered explanation, the answer is no.