"Destroy the world" can mean many things. There aren't nearly enough nuclear weapons to blast Earth itself, the planet will continue to exist, of course.

The raw destructive power of nukes may not be enough to kill most of humanity, yes. Targeted on major cities, it'll still kill an enormous amount of people, an overwhelming majority of the targeted country for industrial (ie, urban) countries.

But that's forgetting all the "secondary effects" : direct radioactive fallouts, radioactive contamination of rivers and water sources, nuclear winter, ... those are pretty sure to obliterate in the few next years most of the remaining humanity. Maybe not all of us. Maybe a few would survive, in a scorched Earth, without much left of technological civilization. That's pretty much "destroy the world" to me.