So what's the criteria for ascertaining that a company, like Twitter, has a monopoly on speech and why does that make it like a government? Unless you are claiming that the US government has a monopoly on speech - meaning that anything the US government does not want said, cannot be said in public which is certainly not true in this case since the head of the US government is threatening to shut down Twitter over something they "said".
> So what's the criteria for ascertaining that a company, like Twitter, has a monopoly on speech
There's no hard criterion, but YouTube is a great example; it is so dominant in the video industry that either you use their service, or almost nobody will see your videos. Facebook is another one - it is now the only social network of its type, and also owns Instagram. If your content is banned from Facebook and Instagram and YouTube and deranked on Google Search, your audience reach will drop to almost nothing. Just two companies control the majority of speech on the western internet.
Twitter IMO doesn't fit into this pattern; it is quite good with free speech. Richard Spencer still has a Twitter account!
The US government deliberately limits its speech monopoly via the 1st amendment, but outside that that limitation it does have a speech monopoly enforced by prison sentences.
Sheer size is a form of monopoly and government. If a company can't be tipped out of your position by a scrappy startup like Youtube, arguably Twitter, then the people have to step in to start making decisions about what it gets to do.