World War in the sense of nuclear weapons and the whole West at war.

Even if it stays that way - Russia against the West - and even if on paper Russia will lose since they are alone - nukes can fly especially over Europe. I'd understand why someone would call that a World War.

There is also a formality in the definition of war vs "special operation". When Russia formally declares war against Ukraine, the West will be considered a cobelligerent if they supply Ukraine with weapons. The partial mobilization is a step towards that