Censorship by a state would include reading mail/e-mail, controlling what is said on social media, controlling what is published in newspapers, what is broadcast on television or radio.
That's problematic. And that's clear censorship.
What you describe is far more murky territory.
If I build a public database which curates newspapers in my local region and I decide to not include a particular outlet, am I engaging in censorship? Not really. As a private actor, it's my prerogative to curate by my own standards. Moreover, one can always go to the library and find that journal in their holdings.
The same principle is true at the scale of search engines. These aren't public institutions. These are private enterprises. They are free to curate content in their own particular fashion. And if one doesn't include your website, well, others might and will.
The issue here isn't that Google doesn't show the website in the search results.
The issue is that Google dominates the search market, and has locked the attention the usage and the vast majority of people using the Web/Internet.
That's a different issue which has less to do with censorship, and everything with being able to establish and hold a monopoly in a particular yet massively important market - information dissemination and communications - for almost 2 decades.
Ask yourself this: Would you or the author of that tweet have made the same loud objection if a website didn't appear in DuckDuckGo?
Why should google link out to a site known to help organize a violent march against democratic processes? Yes Google censors search results, this is nothing new. The only issue you seem to have is that this time instead of it being some ISIS people getting hit its some larping Nazis that performed an actual attack.
Google can choose what is served from their index, end of story. Anyone saying otherwise is tyrannical. If you don't like the results you are getting use something else.
> Google can choose what is served from their index, end of story
And the people can demand that google be broken up into bite sized pieces to promote competition - as we are currently seeing in the DOJ case against google
>Why should google link out to a site known to help organize a violent march against democratic processes?
Source? That's not AT ALL what happens on sites like these (imageboards). These sites have the same risk of having a few psychopaths as sites like Facebook. Actually there are more on Facebook. And these sites have moderators. Do your own research. Browse for awhile and you'll see how ridiculously the reality is different from what you've been getting from the mass media. That's why these sites are censored. Not because there are criminals plotting schemes on them, but because the discussions there are so against the "official" narrative that there are people scared that more and more will realize just how brutally they have been lied to by governments, wealthy organizations, etc.
Google does that all the time.
At the rate this is going, I think we're soon going to see spammers self-righteously denouncing the censorship of their websites.