"Silencing" Is A Communicable Disease
Regarding people with big platforms (like columns in major newspapers) who say they're being silenced, "Is it possible for these people and their opinions to be simultaneously "silenced" and also widely expressed?" asks Tom Chivers at UnHerd:

Obviously, if we take the word "silenced" to mean "literally made silent; unable to put their words out into the world at all", then none of the above has been silenced . Their words are out there.

But if the only people who have permission to complain about being silenced are the ones who are literally silenced, then - by definition - we will never hear about it. I would say it is perfectly possible for people to try to silence you. They might even be successful at partially silencing you, or reducing your output, or making you nervous to say things - even if they aren't able to shut you up entirely. And I would say that even if they aren't successful in the specific case of the famous person involved, it can still have free speech implications for other people.

...In 1989, the novelist Salman Rushdie's book The Satanic Verses was the subject of a fatwa by Ayatollah Khomeini. He spent several years in hiding, under police protection; a $3 million bounty was offered for his death (with an extra $600,000 being added in 2016). The Japanese translator of the book was murdered; the Italian translator was stabbed, and the Norwegian publisher was shot, although both, mercifully, survived.

...To reiterate: I'm not saying that Suzanne Moore or the 'Intellectual Dark Web' are equivalent in any sense to Rushdie, or that they have been subject to the same level of threat as a fatwa and $3 million bounty. The point is that, if you accept that Rushdie was in some sense being "silenced", then you acknowledge that it is possible for people to be simultaneously highly visible, with a platform to say the things they want to say, while also having their free speech curtailed: that it is possible to shout, truthfully, that you are being silenced from the front page of a national newspaper.

Of course, you may not accept that Rushdie was being silenced. This would, in fact, be a fairly reasonable position. The stated aim of the fatwa was not to silence Rushdie, to get him to retract the book, or anything - it was to kill him. According to Khomeini's office, media reports that the fatwa would be lifted if Rushdie apologised were false: "Even if Salman Rushdie repents and become the most pious man of all time, it is incumbent on every Muslim to employ everything he has got, his life and wealth, to send him to Hell."

And this brings us to a second point. I'd say that there probably was a chilling effect on Rushdie himself, but you may disagree. But again: the point was not to silence Rushdie. It was to silence other people. In 2006, after the controversy about a Danish newspaper publishing cartoons showing images of Mohammed, the leader of Hezbollah expressed regret that the fatwa had been unsuccessful: "If there had been a Muslim to carry out Imam Khomeini's fatwa against the renegade Salman Rushdie, this rabble who insult our Prophet Muhammad in Denmark, Norway and France would not have dared to do so."

...Which brings us to the final point. I think that it is possible to be both loud and silenced; and I think that in some cases, even those which fall short of the Rushdie standard of death threats and assassination attempts, it is reasonable to say that this has, in fact, happened.

...Someone can be prominent, and famous, and regularly appear on the television - and they, or their views, or people like them, could still be being silenced.