When a nasty political problem (like the current SSC situation) hits my consciousness, I'm habituated to Do Something About It. I feel an urge to investigate the political climate, find allies, and fight back against the threat. In the current Internet age, and with my nonexistent political clout and social influence (especially considering I live in Iran and people here generally can't be counted on to know or care about global politics), the substitution bias kicks in; I substitute doing The Real Thing (to which my contribution would be very meager if any) with reading online forums (Reddit, Twitter, Lesswrong, SSC, Hackernews, ...)(substituted for "investigate the political climate"), voting the Correct posts in said forums and possibly writing some low-effort answers to particularly egregious pieces ("find allies, and fight back"), and generally feeling bad that I have failed the Mission (and that the Society is broken).
I speculate that this fallacy probably has some evolutionary roots. In a hunter-gatherer tribe, a person such as myself (I estimate myself to be upper-mid status.) would have had a fair chance of affecting political change against causes that mostly hurt everyone but a minority of politicians who don't produce much value anyways. Especially since I (and my family) have been quite morally upstanding and honest, in a small community, we would have had a reputation to draw on. Even if not, engaging with the community would have been the essential first step in being part of a coalition, necessary for survival.
Obviously, in the 21st century, all this is moot for political stuff that actually matters. Most people are quite powerless in affecting those matters, one reason being that the important issues now affect orders of magnitude more people. I don't know what the optimal strategy currently is. My gut feeling is that a lot of the good people are un-politicizing themselves and simply giving up. (Hasn't Scott's default defensive strategy been more (self)censorship?) Individual contributory power being what it is, this might actually be the best heuristic. If political "activism" consists mostly of low-skill low-reputation noise-making, a game of quantity over quality, then "good" people will immediately lose the comparative advantage. In fact, in Iran, the situation seems to be that the only marginally effective activism is violence. Which, in an authoritarian regime, obviously leaves the hungry and the criminal to fend off the evil. The second derivative of their numbers being positive because of abject government failure does not exactly lend me hope.
To summarize; The old-world politics fallacy is the mistaken alief that you have meaningful political power in the 21st century. It often manifests via the substitution bias as fervent but ultimately zero-impact digital activity. Obviously, the fallacy leaves a bitter taste when you do notice that your efforts bore no fruits.
A related phenomenon might be our largely unwarranted interest/motivation (the two are subtly different) for participating in social media that engage mostly with strangers. We are wired to find coalitions of like-minded people and join them, because like-minded people's values align better with our own. The modern era, by allowing our freedom and individuality to flourish, has allowed us to be ever more different than one another. Social media empower us to find and communicate with people much more precisely than is possible in the physical world. These two trends cause us to seek coalition-building in the cyberspace, when the cyberspace usually does not facilitate that function (yet). This will, necessarily, cause us to overvalue our social media interactions. (Because we have the alief that we are actually accumulating social capital when no such thing is happening.)
I don't know what to call this cognitive error. "Pseudo-socializing?"