As far as the wording goes; it doesn't suggest that platform owners have a right to filter content. It suggests that other users (and communities) have a right to filter content.

Though, that right of platform owners to moderate content still feels valid, and I believe this is relatively easy to reconcile. If you believe in this manifesto, then you should draw the conclusion that Platform Owners cannot coexist with it. Companies like Twitter, Facebook, etc; they simply cannot exist in a world where these rights of individuals are respected. Fundamentally, they have to ignore some of these rights in their effort to police and keep control of their platforms.

If you look at something like Mastodon, the situation becomes clearer. There are "platform owners" but they do not control the entire network. They only control that server, and thus the community on that server, yet the servers are still capable of communicating with one another. Reddit is also kind of like this; not to the same degree, but the same idea of "sharded, opt-in moderation" applies (though obviously they do global moderation as well).

Also, tangentially related: Company's rights should never supersede People's rights.