Who is wrong?
Apparently nobody directly, because as it turns out the article only addressed the atmospheric shielding efficiency as related to the initial explosion and gamma blast (so about a month). It was not accounting however for:
- That the capacity of the atmosphere to absorb radiation wasn't infinite and could get exhausted.

Once again we see the potentially fatal consequences when the physicists forget that radiation interaction with matter leads to a non-equilibrium system.   

After a long time some relevant updates to this. The Kurzgesagt Youtube popular science channel just had a video on the deadliness of close Supernovae, and posed them as way more threatening as the previous article that Steve quoted would let you conclude.
Video here:

Looks like coincidentally Veritasium has recently released a video about the same topic (although he seems to focus more on explaining how supernovae are caused):

I haven't done an update in a while, so I probably haven't made this clear.  The Torqual, Doraz, and Zir are all HT-8 right now, and all three recently achieved that tech level.  The Alliance recently reached HT-10.  To be amalgamated into the Alliance, the associates have to be at an equivalent tech level, so it will be some time before they can be integrated.  The Alliance is helping all three with their research efforts, but even so it will take time.

I always used the house rule that was suggested somewhere of when you uplift a low tech race (pre-ind, ind1 or ind2) you bring them to your tech level otherwise they were pointless fluff, and GFFP kicks in (for the uninitiated that's Genocide For Fun and Profit - basically wipe hem out and steal their stuff and planet).  The rational being why teach them transistors when you can teach molycircs.

Can't remember the official rules for a helping a HT race, but I'd probably do something similar, either a direct bump up or otherwise massively accelerated R&D, otherwise the time it takes can be longer than a normal game.

After a long time some relevant updates to this. The Kurzgesagt Youtube popular science channel just had a video on the deadliness of close Supernovae, and posed them as way more threatening as the previous article that Steve quoted would let you conclude.
Video here:

Now, the video is quite sensationalist in its visuals and speech, while it doesn't directly make clear what on every stage actually ends up killing life on the planet. Luckily, the team consists of actual scientists and puts credibility high and thus always provides a very thorough list of their sources, even relating them to the lines said in the video.(sometimes with relevant equations and results on spot)
So the video contrasts the previous findings of the article that let to conclusion that even if Alpha Centauri were to somehow explode, it wouldn't really affect us. Instead, Kurzgesagt states that deadly consequences begin at 150lys already. Who is wrong?
Apparently nobody directly, because as it turns out the article only addressed the atmospheric shielding efficiency as related to the initial explosion and gamma blast (so about a month). It was not accounting however for:
- That the capacity of the atmosphere to absorb radiation wasn't infinite and could get exhausted.
- A late wake 'radioactive tsunami' caused by the interstellar gas simultaneously being compress-pushed away and ionized, which will propagate further (but lower) radiation for unforeseeable timescales. (interestingly, the radiation from this will remain almost constant even with the wave approaching. Only if it should hit will there be a serious spike)
- The most important point: Secondary source damages relating to the stripping away of Ozone as this layers' capacity is among the first to be overwhelmed. (there are other consequences stemming from UV, but this is enough)

..And that is basically what the video boils down to. It is not the supernova radiation killing directly, so no dramatic "explosion kills" or 'zap-cancer'-radiation flashes, but it stripping thin Earth's shielding and thus exposure to solar UV and other cosmic radiation that ends up killing everything, ...but over some time.
Especially the sensationalist 25ly 'kill radius' from the video specifically relates to a much more tamely formulated article of USA National Academy of Sciences that simply calculates and mentions that the breakdown of Ozone at these intensities would persist for some hundreds of years, which would upend the base of the foodchain in plankton and thus cause total collapse and a mass extinction event.

So in conclusion: The supernovae are still not really killing through their own radiation directly, although they even might do that if they can overwhelm atmospheric capacity. (sadly I found no source in here that clearly stated at which levels that would happen for Earth) Instead, the most concerning effects are related to the destruction or even just partial suppression of the most vulnerable atmospheric layers.
..That however means that the final enemy in a near supernova event would actually be a planet's own star, not the supernova, and thus radiation damage should scale by the own star's parameters.

Anyway, that might all be too detailed to model in a game. In the end it does not matter who does the damage for simplification's sake. I would just say that lasting radiation doses, and even deadly supernovae are confirmed in the 150ly and 25ly range. It is no cool explosion, but I retract my previous joking of them being mere "christmas lights" as well.