Is the subtext that Putin plans to blow it up, or what?
Information war does not need a rational subtext - I suspect it is more effective when it hasn't any. Even better if multiple rationalities are all slightly plausible yet all slightly absurd.
The fundamental tactic is to obscure truth with a flood of bullshit. One thus removes the surety of known & agreed facts from both the politics of enemy's polity and the planning of the enemy's military.
With its rapidity, and its dynamic reaction the the enemy's information disposition, Russia's approach is to conventional propaganda what blitzkrieg was to trench warfare - largely the same tools, but radically different tactics. To stretch the analogy, the internet takes the tank's place as the key disruptive technology which both inspires and requires new tactics.
I'm pretty sure that attacking central Europe with a dirty bomb would make it very difficult for NATO to avoid invoking Article 5.
This threat is, I'm pretty sure, not intended. Russia already has enough nukes and Putin has already rather clearly threatened nuclear escalation if any nation "interferes." There is perhaps an implicit threat intended - "nice continent you got here - and, oh, look, Russia is now in charge of protecting its on-going habitability!"
Think of it like this:
Russia wants to be a respected great power. Putin's revisionist fantasy casts Russia as the primary arbiter of Europe's political order.
Chernobyl is an on-going danger to the entire peninsula's safety. It must have a robust institutional custodian - perhaps for centuries to come. It may not be as dangerous, but that cannot be assumed, it must be proven conclusively (and even then concern will linger: democracies are quite skilled at turning society's vague, broadly-held fears into irrational policy).
Therefore Europe cannot ostracize any polity controlling the exclusion zone indefinitely. The EU paid for the current sarcophagus: managing this risk is a vital interest of the entire Union.
More broadly: fear need not be (and usually is not) rational in order to be acted upon - especially in democracies.
Pripyat and its immediate vicinity is just an unpopulated area with a decomissioned nuclear power station in it.
You are rational and informed, and perhaps correct (I don't know). As far as facts actually matter here, however, your analysis is incomplete.
The exclusion zone is an unpopulated area with a decommissioned nuclear power plant *which happens to be directly between the Russian army and their objective*. Any conventional attack on Kyiv from Belarus must include this area - even if it was truly unexceptional.
But the facts don't matter. "Chernobyl" is a totem in American and European minds. The very fact of this HN post's popularity attests such.
Russian strategists hope, I think, that they can gain an edge by capturing the totem. They think to turn its symbolic meanings to their own ends.
Ukrainians also hope to use Chernobyl's various meanings in the minds of their allies to their advantage, as a warning and an impetus for solidarity.
Semiotic warfare, if you will!