:( "cyber" sounds so cool, I feel like the potential of the word has been wasted after popular culture turned it into a meaningless fugazi.
all have Latin roots, so your proposed rule of thumb doesn't even work on your own examples. (And some might even consider a single app or game a cyberspace.) is the exact same word in any context, and it is only from that context that you can tell if it means "the theory/science of communication and control in the animal and the machine", "the art/study of governing, controlling automatic processes and communication", or "technology related to computers and Internet".
You shout mean things into the air and physics makes sure your overbearing soundwaves propagate to your target.
Bo that would mean that pretty much everything is cyber-, because everything is controlled by something.
According to Etymology Online it comes from Cybernetics, which in turn comes from the greek for "Helmsman" and is the study of governation or governing systems.
And a cyborg can sit on the subway next to a cyberterrorist, but that's about as much as they have in common.
But modern usage, such as cyberspace, cybercafe, cyberattack, cyberterrorism, cybermosque, cybersex, cyberbullying, and such seem to use it synonymously with "Internet" Of course, you could argue that you use a cybercafe to interact with a primitive virtual governor, a cyberspace is a place where a lot of virtual governors "reside", while cyberattacks try to disrupt these governors.
But cyberbullying and "cybering" really don't fit into that scheme, unless you were to day that cyberbullying is "bullying by relaying domineering or intimidating messages with the help of a governor." but then again "physics" could be a governor.
Looking at the etymology at that point is at best useless, and at worst an etymological fallacy.If you don't like my invented example and think it is an exaggeration, try and find a hypernym for "door", "passageway", and "scandal", which are only some of the meanings happens to mean.