To make an analogy: A musician is no less of an artist because he or she performs as a solo act, rather than as part of a band.
Yet what "the press" means is "the body of news and journalism organisations". It is very possible to have a heavily constrained press, while individuals who are not the press and not part of the press have much more freedom to say what they like into the aether.
Here is what the Swedish National Archive writes on the subject, and I share the same view:
"When freedom of the press was introduced in 1766, many people wanted to express their opinions and spread their ideas. At this time, it was through shorter publications that people could communicate and reach many readers. A flood of printed material emerged, completely uncensored."
Some printers started to print the minutes of the courts to distribute them to the public. This way, people could read and see for themselves how the country was run and information could be disseminated in a completely different way than before. This became a profitable business idea. Freedom of the press and the principle of public access became a weapon for ordinary people against those in power and their decisions."
Not under the common definition of the press. By all means have a different definition, but if you do, it's only fair that you state up front that you mean something other than the common definition.
It's called "the press" because of the printing press. Could you think of some single individuals who have had massive impact on their societies by expressing themselves through printing pamphlets and books?