This would be more persuasive with a cite to evidence that the Google presentation does not, to a first approximation (after the paid advertisements), present links in roughly descending order of frequency of access by their users. They certainly have tweaked it a bit, but it is not at all obvious that a reasonable amount of reordering as a result of algorithm tuning would change the basic indexing operation to "publication" and even less obvious that this would represent human choice when applied to particular instances in a very large collection.
The claim that Google "promotes" certain tweets to the top implies a good deal more agency than is likely to occur. My guess is that tweets wind up at the top largely because they are retweeted a lot, as will likely happen with those that are startling or cater to widespread stereotypes or biases.
Accepting advertisements from foreign entities relating to matters discussed in a US political campaign, including RT but certainly not limited to either it or Russian entities, appears not to be illegal in general. Accepting "electioneering communication" may be illegal, but what has been reported about the ads in question, whether to Google, Facebook, or Twitter, seems not to be "electioneering communication" as the term is used in the US Code and Code of Federal Regulations.
Whether Google and similar portals damage the traditional news media is uncertain. I seem to recall that several Google deindexed some European news organizations that demanded payment from them in exchange for indexing; and my recollection, if accurate, is that the traffic to those sites dropped immediately and dramatically, to the point that the organizations dropped their demand within a few days. It is clear that printed news media are in a long term secular decline as more people get their news from online sources. That is a potential problem, to the extent that the online sources such as Breitbart are able to compete effectively with the much more expensive operations of traditional news organizations like the New York Times which have news staffs that actually seek out and report news. I do not know the ultimate answer to that, but try to do my part by subscribing to the New York Times, the Washington Post (online), and a local newspaper.
The notion that we might "need to force Google to take on some of [the traditional news media] fact-checking" cannot be taken seriously. It might be legally possible in some countries, but not in the US, where the first amendment largely prohibits the government from requiring it.
One might think this could be circumvented by requiring those, like Google, who provide easy access to articles that may contain lies and misstatements, to check facts and screen out false statements. On cursory consideration, though, that seems unlikely to be practical. Even if legislated, it would place Google and the others in the position of being editors and publishers, and therefore exempt under the first amendment. Moreover, such a requirement would be easily enough circumvented at the source, simply by following the example of the New York Times, Washington Post, Fox News, MSNBC, and other traditional news organizations to present the facts fairly accurately in a slanted context of emotionally loaded words to convey an implicit message about goodness or badness. The article ahead of of this comment string is a case in point.