In effect they do set rules for the Internet as a whole, though. For instance, if you're the owner of (say) a news website, Google don't want you to host text ads that contain live links because their entire search engine is based around the assumption that links are non-paid. So they penalized a number of major news sites for doing this, effectively forcing them to stop by taking away one of their main sources of traffic.
Sure, but, arguably, those rules are "correct". The fact that they run the leading search engine implies that they provide the best quality (or at least best perceived quality) search results. Those rules presumably contribute to that.
> Their product has a monopoly in most of the world.
Yeah.. it really doesn't. The DoJ would be all over their ass if there was really a case to be made there.
> Therefore it's a rule for the internet.
That doesn't even logically follow if we assume the first. It is more than possible to use the internet without giving a shit about google's product. Even if it were a monopoly this would be true.
Google changing how their product reacts to RapGenius does not effect anything other than how their product reacts to RapGenius. Just because RapGenius cares a lot about how Googles product reacts to their own does not mean that the rules of Googles product are rules "of the internet".
If Google had the power to set "rules of the internet", then the MPAA/RIAA would have won their battle when Google changed how their product handles search results for torrents. Of course they did not, because Google cannot.
> Yeah.. it really doesn't. The DoJ would be all over their ass if there was really a case to be made there.
This just shows that you don't understand what a monopoly is. Monopolies are not in themselves illegal, so there is no reason for the DoJ to get involved unless they break one of the laws regarding what monopolies can and can't do.
And, of course they are being investigated for doing exactly that in Europe.