I think the overpopulation in that article is more in the Pacific Ocean. The way it was explained to me (in Spanish, and I'll admit I'm not exactly fluent) was that squid fishing off the coast of Argentina and nearing Antartica is not at all regulated and they use much bigger and more powerful lights to attract them than what they'd be permitted to use elsewhere.

I don't think they're technically "allowed" to use those sorts of lights in Southern Ocean either but each nation is responsible for enforcing the treaty and most governments don't. It's also my understanding that Japan is pretty open and notorious in their Antarctic fishing in violation of international treaties but everyone just sort of shakes their head without doing much to stop them.

Edit: Not particularly detailed but mentions the lack of regulation/overfishing in the area: https://www.theguardian.com/lifeandstyle/shortcuts/2016/oct/...