Maybe at some point it was, but we are well past sbux owning the term. You can see for yourself, do a google search for "third place -starbucks" and filter down to results in the last 24 hours. You will still find news articles, reddit threads, etc, using the very same definition we are using here.

I've seen articles in strong town use it, I've heard the term come up in meetings of my local pro-development citizen's organization, etc. Starbucks has no claim to the term third place, especially given that since covid, the majority of them don't even qualify as third places.