I consider it terrorism when the intent of the act is to hurt or kill people. I think most people, beyond those being deliberately pedantic, define it the same way.
The other problem with your definition is that, while it may help distinguishing terrorist actions from other actions, it does not help drawing the line on what kind of communications "are terrorist" or "promote terrorism" to censor? There are many tricky questions, for example:
- Do you censor everything that a terrorist group says, or only whatever explicitly advocates terrorist tactics?
- Do you censor sympathizers with the terrorist group?
- Do you censor people that share the ideas of the terrorist group? Even if they do not defend them with violence? But what if they do not promote violence but they do not publicly condemn the terrorist group?
Etc, etc.
As you can see, the question is tricky. In Spain this debate has been alive for years with regards to the basque independentist group ETA. This was often a mess, with even certain independentist newspapers being prohibited at times. Sometimes these actions made ETA recruiting easier indeed--it's easy to argue that violence is your only alternative when your political voice is censored. In most absurd cases, people that are not even independentist or anything alike are being prosecuted for posting jokes involving ETA on Twitter.
So, it's not about being pedantic. Discriminating what kind of media promotes terrorism and not is hard. The political implications of censoring are huge, and there can be unintended consequences. It basically means drawing a clear political line on the limits of freedom of speech.
I would be afraid if these lines are drawn by private entities, secretly, without a public debate on what is tolerable or not, and with the public not even knowing whether they are being censored or not.
Let's also remember that in the context of Google and Facebook, we aren't talking about censorship by the government, or private organizations setting laws that all citizens must abide by. These are private organizations that are free to censor anything they wish, and to define their own terms of service. What they are doing seems to be a socially responsible move. People that are unhappy with these services are free to publish their stuff elsewhere.