> It obviously can't be true since end of the world in any reasonable understanding contains end of the internet.

No, it obviously can be true. I can imagine many ways "the end of the world" could occur. Also, maybe it's not crystal clear what "the end of the world" means to you, but for me, and likely other people, it means the collapse of human civilization, which could happen from nuclear war, climate change, etc.

Just because "the end of the world" would include "the death of the internet" doesn't imply that by imagining the end of the world you're also imagining the ways in which every aspect of the world get destroyed. When I imagine the end of the world I don't focus on what happens to say, Paris, specifically, but I do know, implicitly, that the end of the world would include the end of Paris.