No, the first amendment of the constitution of the United States (which describes the US government's responsibilities in regards to freedom of speech) has nothing to do with Reddit. Freedom of speech as a concept can be applied to anything: reddit, the government, hacker news, you or I.
American corporatism and singular definition of 'freedom of speech' as being 'the amendment' really polluted the well of any discussion of the topic on English-speaking platforms.
We, in Europe, have limited freedom of speech. You can't do things like denying the holocaust. But that doesn't mean we don't recognize the concept of freedom of speech, and that we don't have discussion platforms that feature freedom of speech -within the limits of our laws-. Censorship is still censorship, even when it's done by a corporation.
Listening to americans there can be no debate as to whether censorship even exists if it's done by a corporation because corporation are free to do anything and we shouldn't even debate what they do and whether we should boycott a place and move onto something else because corporations can do no wrong and exerting individual judgement, opinion, and sharing them, encouraging the growth of freer online platforms and the likes is heavily discouraged. No, everything has to do with the law and if the law doesn't call it bad then it's not bad and it shouldn't be judged as bad. That worship of the law and constitution as the only sacred values in human societies is disgusting.