You see the reading “the press” as meaning some organization of people. You take it for granted that the freedom of the press applies to a business entity like the NYT and also to an individual blogger or any other person creating a publication.

The idea that people can come together to form cooperative groups and can use those to exercise rights through the idea of personhood is such a normal and legally settled idea.

The New York Times (the corporation, as a legal person) has the right to freedom of the press, not just individual humans who work there. This is good, because it means the entire institution is protected. Not only is the government forbidden from arresting the humans for operating the printing press, it’s also forbidden from sanctioning the corporation for hiring humans to operate the press. In other words, freedom of the press applies to corporations (eg. the Times) as well as human persons. I think you and the commenter you responded to both agree on the fundamental claim here, although you might disagree about the semantics of whether “corporate personhood” is a good way of describing this concept.

A restriction on government (as the First Amendment language is phrased) is not the same thing as an individual right. There are plenty of cases where a restriction is in the law, but only a very limited set of entities has standing to sue to enforce it. You could imagine such a case with regard to the First Amendment if we didn't have the corporate personhood doctrine.

It's about the dichotomy. If the NY Times has First Amendment rights then Pfizer does.

That annoys people because Pfizer is going to advocate for things some people might not like. But that's the cost of a rule that makes it so the NY Times can advocate for things other people might not like.