"Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof; or abridging the freedom of speech, or of the press; "
At the time this was written, there was no class of professional, full-time reporters referring to themselves as "the press". In this context, "freedom of the press" is freedom to disseminate your opinions via the written word, like you and I are doing now. In the 18th century, it was common for people to hire a printer to make pamphlets for distribution. See the history of the "Federalist Papers".
"Freedom of the press" applies to ALL Americans, not just full-time professional journalists.